Is it true, Pamela?
- Thread starter CatJammin
- Start date
Re: Royal Airforce contact me about John
Cig,
I was a lurker on many fourms. Some of them I never posted on. I have post on a few though. I think there are lots of people who only read here and never post. Some of them may be real time travelers. LOL
No one has really proven to be the real deal. I have read some very good tales of time travel on the internet. There always seems to be flaws in the story.
If Mrs. Clinton is not elected president next year. There goes many of these storys out the window.
What if the winner of the next presidental election has not announced they are running?
Cig,
I was a lurker on many fourms. Some of them I never posted on. I have post on a few though. I think there are lots of people who only read here and never post. Some of them may be real time travelers. LOL
No one has really proven to be the real deal. I have read some very good tales of time travel on the internet. There always seems to be flaws in the story.
If Mrs. Clinton is not elected president next year. There goes many of these storys out the window.
What if the winner of the next presidental election has not announced they are running?
Re: Royal Airforce contact me about John
OH yea I noticed a limited amount of regular posters. Such is they way of every forum and I am happy to toss my lot into the participant sections of members here at this forum. Your welcome.
SO back to the question of whats the point? Py-op..maybe but why? What would be the psy-op goal? This also fails to explain why the operstion started up in 98 with two faxes then went on hold for two years.
I pyschological game..again 4 years in the ploting...Thats a long time to wait for a pay off.
An operation to search for domestic terrorists...This on explaination is most laughable considering that giant computer banks monites every sent keystroke and record flaged words for further examination under the warrentless wire tap operations and patriot act stuff. Not to mention Titor story was told in the magical time before Terrorists hid behind every corner and fire did what only controled demolition has been able to do before and since. So no a domestic terrorist sting operation is defintily out.
Gang stalking...People generaly stalk with an expactation of getting something eventualy. And again thier is the 98 faxes to explain away.
So no my buble is not burst.. No need for apoligies. When I insist on a full explaination I accept nothing less.
Eric
If a presidential hopeful has not yet annouced thier bid for president they might aswell not bother.
OH yea I noticed a limited amount of regular posters. Such is they way of every forum and I am happy to toss my lot into the participant sections of members here at this forum. Your welcome.
SO back to the question of whats the point? Py-op..maybe but why? What would be the psy-op goal? This also fails to explain why the operstion started up in 98 with two faxes then went on hold for two years.
I pyschological game..again 4 years in the ploting...Thats a long time to wait for a pay off.
An operation to search for domestic terrorists...This on explaination is most laughable considering that giant computer banks monites every sent keystroke and record flaged words for further examination under the warrentless wire tap operations and patriot act stuff. Not to mention Titor story was told in the magical time before Terrorists hid behind every corner and fire did what only controled demolition has been able to do before and since. So no a domestic terrorist sting operation is defintily out.
Gang stalking...People generaly stalk with an expactation of getting something eventualy. And again thier is the 98 faxes to explain away.
So no my buble is not burst.. No need for apoligies. When I insist on a full explaination I accept nothing less.
Eric
If a presidential hopeful has not yet annouced thier bid for president they might aswell not bother.
Darby
Epochal Historian
Re: Royal Airforce contact me about John
ruthless,
I'm not in the entertainment business so I really can't define for you, or anyone else, "where's the money here" in the Titor Saga. All that I can say is that Larry Haber is in the entertainment business and for whatever reason he can see a potential upside.
I've dropped in the URL for the Florida Department of Corporations below. Go to that page and list "Haber, Lawrence" as your search criteria. Look at the output for Lawrence and Lawrence H. Haber. It's page after page of entertainment/movie projects that he's been involved in. He's been a top attorney for both Disney and Universal Studios. He knows what he's doing. It's not a slam dunk but he apparently believes that it's worth his time to be involved (assuming that he's not Titor - which isn't in itself a sure bet).
http://www.sunbiz.org/corioff.html
ruthless,
I'm not in the entertainment business so I really can't define for you, or anyone else, "where's the money here" in the Titor Saga. All that I can say is that Larry Haber is in the entertainment business and for whatever reason he can see a potential upside.
I've dropped in the URL for the Florida Department of Corporations below. Go to that page and list "Haber, Lawrence" as your search criteria. Look at the output for Lawrence and Lawrence H. Haber. It's page after page of entertainment/movie projects that he's been involved in. He's been a top attorney for both Disney and Universal Studios. He knows what he's doing. It's not a slam dunk but he apparently believes that it's worth his time to be involved (assuming that he's not Titor - which isn't in itself a sure bet).
http://www.sunbiz.org/corioff.html
Darby
Epochal Historian
Re: Royal Airforce contact me about John
titorite,
As I said, it's not a secret. All you have to do is buy the site if you really have to know the information. That's your call to make, not mine.
As to the "I got the proof but Im not sharing(TYPICAL!)" isn't that precisely what Titor said - adding that he didn't actually care if you believed him and preferred that you didn't?
It cuts both ways. In one case you use the ploy to undercut a statement. In your preferred case you use it to proove your belief in Titor. Why is that?
Anyway, if you truly want to know the answer you can have it - but you will have to pay to play. How curious are you? How much stock are you willing to put up considering that you believe the story and thus know that even if you borrow the $20k-$25k you'll never have to pay much of it back because the Russians will nuke the crap out of this continent in three years. Dive in - just do it. Borrow the money based on your faith in the storey. There's absolutely no financial risk...if you are as steadfastly convinced as you claim.
Or is their some doubt in your mind?
The ball's in your court. You control your own destiny in this case.
Do it!
titorite,
As I said, it's not a secret. All you have to do is buy the site if you really have to know the information. That's your call to make, not mine.
As to the "I got the proof but Im not sharing(TYPICAL!)" isn't that precisely what Titor said - adding that he didn't actually care if you believed him and preferred that you didn't?
It cuts both ways. In one case you use the ploy to undercut a statement. In your preferred case you use it to proove your belief in Titor. Why is that?
Anyway, if you truly want to know the answer you can have it - but you will have to pay to play. How curious are you? How much stock are you willing to put up considering that you believe the story and thus know that even if you borrow the $20k-$25k you'll never have to pay much of it back because the Russians will nuke the crap out of this continent in three years. Dive in - just do it. Borrow the money based on your faith in the storey. There's absolutely no financial risk...if you are as steadfastly convinced as you claim.
Or is their some doubt in your mind?
The ball's in your court. You control your own destiny in this case.
Do it!
TheCigSmokingMan
Rift Surfer
Re: Royal Airforce contact me about John
EricCarr and Titorite,
I have told you the truth and the most logical explanations.
If you have been following Darby's posts, he has many times stated it is a GAME. He have also stated once or twice that it is ENTERTAINMENT.
Darby is hinting at what he knows... /ttiforum/images/graemlins/smile.gif
I posted in the "Titor - Track Record To Date" thread the prophecies by various historical figures that "GROUP TITOR" used. They used these prophecies and current events such as physics research projects to give their story the most probable possible outcomes of coming true.
The "Pope" claim that the pope dies IS NOT TRUE. Titor said their would be "ONE MORE POPE"
This is how I knew they were using the "Prophecies of St. Malachy"... Look him up on the internet.
http://en.wikipedia.org/wiki/Saint_Malachy
If you follow COAST TO COAST, the last time DARBY was on... A caller claiming to be a Key Card Technician called in saying he talked to the children of Celebration Fl that stated:
o Their parents were responsible for the Titor Story
o They used 'pyschic' predictions for the story
I don't know how much closer you can get unless you PAY for the sites DARBY is talking about.
You should forget Titor.
As for the paying attention to Internet sites, let me point out the whole DEBKA internet scare carried out in New York City yesterday or the day before...
The SUPER SECRETS pay attention.... But believe what you will...
TheCigMan
EricCarr and Titorite,
I have told you the truth and the most logical explanations.
If you have been following Darby's posts, he has many times stated it is a GAME. He have also stated once or twice that it is ENTERTAINMENT.
Darby is hinting at what he knows... /ttiforum/images/graemlins/smile.gif
I posted in the "Titor - Track Record To Date" thread the prophecies by various historical figures that "GROUP TITOR" used. They used these prophecies and current events such as physics research projects to give their story the most probable possible outcomes of coming true.
The "Pope" claim that the pope dies IS NOT TRUE. Titor said their would be "ONE MORE POPE"
This is how I knew they were using the "Prophecies of St. Malachy"... Look him up on the internet.
http://en.wikipedia.org/wiki/Saint_Malachy
If you follow COAST TO COAST, the last time DARBY was on... A caller claiming to be a Key Card Technician called in saying he talked to the children of Celebration Fl that stated:
o Their parents were responsible for the Titor Story
o They used 'pyschic' predictions for the story
I don't know how much closer you can get unless you PAY for the sites DARBY is talking about.
You should forget Titor.
As for the paying attention to Internet sites, let me point out the whole DEBKA internet scare carried out in New York City yesterday or the day before...
The SUPER SECRETS pay attention.... But believe what you will...
TheCigMan
Re: .
I am just posting to anyone. Hello this is Planet Earth, anyone out there, anyone at all?
There's no Business like Show Business, it's like no business I know.
Everything about it is exciting...............whatever the words are to that song.
Anyway, half of the things posted as Titor stated this or that, has been usually wrong. He did not state most of the stuff some people seem to come up with on their own.
I just suggest that some people actually review what JT stated in the first place, if the name is going to be used to state something about something that was stated by another person already living. As far as anyone knows, JT is not posting.
Oh, there's no business like show business, it's like no business I know.
Everthing about it is exciting and so inviting, so let it show.
(if anyone wants the words to that song, then probably the Internet has those words somewhere.)
I am just posting to anyone. Hello this is Planet Earth, anyone out there, anyone at all?
There's no Business like Show Business, it's like no business I know.
Everything about it is exciting...............whatever the words are to that song.
Anyway, half of the things posted as Titor stated this or that, has been usually wrong. He did not state most of the stuff some people seem to come up with on their own.
I just suggest that some people actually review what JT stated in the first place, if the name is going to be used to state something about something that was stated by another person already living. As far as anyone knows, JT is not posting.
Oh, there's no business like show business, it's like no business I know.
Everthing about it is exciting and so inviting, so let it show.
(if anyone wants the words to that song, then probably the Internet has those words somewhere.)
Re: Royal Airforce contact me about John
Years have gone by. The majority says Titor is a fake becuase this didn't come true or because the physcis theory is false...Nobody is willing to offer concrete proof but they are willing to SELL it. Those with nothing to sell have already concluded in there minds that they have the titor story figured out and they give "best possible explinations" , thier theories but again nothing concrete.
Few seem willing to admit that the poem he spoke of was a one and a trillion shot of getting right.
Fewer still ever want to factor in the 98 faxes. IF they did ,would they consider the fact that the titor in 98 was different from the titor in 2000? Or would they continue to work to fit the story into thier preconcieved ideas of it already being a hoax?
My mind is open. I can be proven wrong but I think I am right. If I am to be proven wrong I need something better than "It is a game and you lose if you buy the story" or "it was a psy-op to hunt for domestic terrorists" or "it was a scam to make money" NONE of that has been proven but many have "assumed" and we know what the military thinks of assumptions.
Darby says he knows the Titor identity but won't revel it. If I had to make an educated guess I would guess that Darby believes Titor to be this Boomer fellow. If that is so why not just ask the boomer (or whoever else it is) to out himself? I mean if boomer(we'll just use that name now for simplicities sake) did it for fun then you can ask him why he stoped in 98 after two faxes? Was it just to lend crediblity to the story? And how did boomer know enough to name the poem? If boomer did it for the money why hasn't he cashed in yet...THIS is the summer to do it considering Hillaries bid for president and all. Thing is since the story is told in words online it wouldn't translate real well to the big screen and even the most amature screen writer understand this basic point. So how could the boomer genius make such a fatal error and yet be so smart in so many other areas?
Is Larry Cluck involved in this hoax too? I mean Larry Harber, Larry Cluck. *IT CAN'T BE COINCIDENCE* <....Flawed reasoning.
At this point I see skeptics reaching at straws putting forth any theory they can to explain away what they can not accept.
Lets Go to where I have gone on this quest.
I have been to 2036 future way celebartion florida. That whole thing is fishy but it fails to explain anything other than disneys plans to capitolize on this...and how they plan to is beyond me.
Jonathan Titus. Others of brought him up either at ATS or anomils and again if this is the guy then why does he deny responsiblity. More then that why would HE do it.
There is a myspace guy he claims to be friends with the John Titor person. He says that JT is a C++ software guy who is a jehovas witness with strong anti government feelings....Any crediblity for this panning out stoped at jehovas witness. More then that the guy haas changed his story from knowing the person to knowing the group...so thats another dead end.
The laser photo itself has been "doctered" from site to site..Meaning in an effort to disprove Titors story based on the photo some enterprising individual altered the original. The proof is in the tail end of the laser.(am I the only one that noticed in some photos the tail is grey and in other photos its not there at all?) Thier is also the differences in luminosity to consider when comparing laser photo to laser photo.
SO I myself have looked to disprove this. But I will not accept idle speculation as proof. To date I have seen more "predictions" come to pass then not. And the physics are there on paper waiting to be tested at CERN.
But by all means if you can bring John Titor to this web site to be verified by Pam do it...if nothing else it sure would increase traffic here and make TTI a few bucks.
Years have gone by. The majority says Titor is a fake becuase this didn't come true or because the physcis theory is false...Nobody is willing to offer concrete proof but they are willing to SELL it. Those with nothing to sell have already concluded in there minds that they have the titor story figured out and they give "best possible explinations" , thier theories but again nothing concrete.
Few seem willing to admit that the poem he spoke of was a one and a trillion shot of getting right.
Fewer still ever want to factor in the 98 faxes. IF they did ,would they consider the fact that the titor in 98 was different from the titor in 2000? Or would they continue to work to fit the story into thier preconcieved ideas of it already being a hoax?
My mind is open. I can be proven wrong but I think I am right. If I am to be proven wrong I need something better than "It is a game and you lose if you buy the story" or "it was a psy-op to hunt for domestic terrorists" or "it was a scam to make money" NONE of that has been proven but many have "assumed" and we know what the military thinks of assumptions.
Darby says he knows the Titor identity but won't revel it. If I had to make an educated guess I would guess that Darby believes Titor to be this Boomer fellow. If that is so why not just ask the boomer (or whoever else it is) to out himself? I mean if boomer(we'll just use that name now for simplicities sake) did it for fun then you can ask him why he stoped in 98 after two faxes? Was it just to lend crediblity to the story? And how did boomer know enough to name the poem? If boomer did it for the money why hasn't he cashed in yet...THIS is the summer to do it considering Hillaries bid for president and all. Thing is since the story is told in words online it wouldn't translate real well to the big screen and even the most amature screen writer understand this basic point. So how could the boomer genius make such a fatal error and yet be so smart in so many other areas?
Is Larry Cluck involved in this hoax too? I mean Larry Harber, Larry Cluck. *IT CAN'T BE COINCIDENCE* <....Flawed reasoning.
At this point I see skeptics reaching at straws putting forth any theory they can to explain away what they can not accept.
Lets Go to where I have gone on this quest.
I have been to 2036 future way celebartion florida. That whole thing is fishy but it fails to explain anything other than disneys plans to capitolize on this...and how they plan to is beyond me.
Jonathan Titus. Others of brought him up either at ATS or anomils and again if this is the guy then why does he deny responsiblity. More then that why would HE do it.
There is a myspace guy he claims to be friends with the John Titor person. He says that JT is a C++ software guy who is a jehovas witness with strong anti government feelings....Any crediblity for this panning out stoped at jehovas witness. More then that the guy haas changed his story from knowing the person to knowing the group...so thats another dead end.
The laser photo itself has been "doctered" from site to site..Meaning in an effort to disprove Titors story based on the photo some enterprising individual altered the original. The proof is in the tail end of the laser.(am I the only one that noticed in some photos the tail is grey and in other photos its not there at all?) Thier is also the differences in luminosity to consider when comparing laser photo to laser photo.
SO I myself have looked to disprove this. But I will not accept idle speculation as proof. To date I have seen more "predictions" come to pass then not. And the physics are there on paper waiting to be tested at CERN.
But by all means if you can bring John Titor to this web site to be verified by Pam do it...if nothing else it sure would increase traffic here and make TTI a few bucks.
Re:
I wonder why Darby keeps ignoring my question. Seems to me he doesn't want to answer it because he
is just taking someone's word on it.
For the third time:
Darby,
I have to ask. Are you just taking this persons word that says he knows about John's IP?
Or have you been shown some kind of actual proof?
I wonder why Darby keeps ignoring my question. Seems to me he doesn't want to answer it because he
is just taking someone's word on it.
For the third time:
Darby,
I have to ask. Are you just taking this persons word that says he knows about John's IP?
Or have you been shown some kind of actual proof?
Darby
Epochal Historian
Re:
Pamela,
Yes, I've avoided answering. You're rubbing up against the same territory that you avoid answering questions about and for similar reasons, if you know what I mean.
You know that this isn't new information. We received it years ago. But so far no one seems to be curious enough about the information to take the plunge. As I said, I'm not curious enough to spend $100 let alone $20k-$25k to buy an entire website.
Pamela,
Yes, I've avoided answering. You're rubbing up against the same territory that you avoid answering questions about and for similar reasons, if you know what I mean.
You know that this isn't new information. We received it years ago. But so far no one seems to be curious enough about the information to take the plunge. As I said, I'm not curious enough to spend $100 let alone $20k-$25k to buy an entire website.
Darby
Epochal Historian
Re: Royal Airforce contact me about John
CigMan,
It's not just a hint it's the fact based on the evidence in front of our eyes. Titor comes along to both destroy and save the world along with saving one set of an infinite set of alter-parents/self (if you buy into Titor's particular flavor of Internet pop-sci quantum mechanics).
And what does Mom Titor do? To protect her family from Big Bad Govmit by remaining anonymous and quietly under the radar in Colorado...she hires a Disney/Universal Studios attorney to headquarter the JTF in a movie studio, graphic arts studio, sound studio. Thereafter...The Book, The Radio Program promo, The Movie, coffee mugs, t-shirts, JT Fan blitzing a thousand sites in a single week on the WWW and UseNet with Titor spam, Buzzmaker making a visit to Anomalies, Larry Haber making a post here and there (and all of them using the same email addy and IP, BTW), etc.
That's Entertainment - and I don't have a real problem with any of it. I've been entertained for seven years. Yes, my friend - it's a game with the intent to make a buck. /ttiforum/images/graemlins/smile.gif
CigMan,
It's not just a hint it's the fact based on the evidence in front of our eyes. Titor comes along to both destroy and save the world along with saving one set of an infinite set of alter-parents/self (if you buy into Titor's particular flavor of Internet pop-sci quantum mechanics).
And what does Mom Titor do? To protect her family from Big Bad Govmit by remaining anonymous and quietly under the radar in Colorado...she hires a Disney/Universal Studios attorney to headquarter the JTF in a movie studio, graphic arts studio, sound studio. Thereafter...The Book, The Radio Program promo, The Movie, coffee mugs, t-shirts, JT Fan blitzing a thousand sites in a single week on the WWW and UseNet with Titor spam, Buzzmaker making a visit to Anomalies, Larry Haber making a post here and there (and all of them using the same email addy and IP, BTW), etc.
That's Entertainment - and I don't have a real problem with any of it. I've been entertained for seven years. Yes, my friend - it's a game with the intent to make a buck. /ttiforum/images/graemlins/smile.gif
ruthless
Rift Surfer
Re: Royal Airforce contact me about John
"And what does Mom Titor do? To protect her family from Big Bad Govmit by remaining anonymous and quietly under the radar in Colorado...she hires a Disney/Universal Studios attorney to headquarter the JTF in a movie studio, graphic arts studio, sound studio. Thereafter...The Book, The Radio Program promo, The Movie, coffee mugs, t-shirts, JT Fan blitzing a thousand sites in a single week on the WWW and UseNet with Titor spam, Buzzmaker making a visit to Anomalies, Larry Haber making a post here and there (and all of them using the same email addy and IP, BTW), etc."
ty sir, you just answered a butload there, makes all the sense in the world now.
btw, i thought it was larry's kid once...
"And what does Mom Titor do? To protect her family from Big Bad Govmit by remaining anonymous and quietly under the radar in Colorado...she hires a Disney/Universal Studios attorney to headquarter the JTF in a movie studio, graphic arts studio, sound studio. Thereafter...The Book, The Radio Program promo, The Movie, coffee mugs, t-shirts, JT Fan blitzing a thousand sites in a single week on the WWW and UseNet with Titor spam, Buzzmaker making a visit to Anomalies, Larry Haber making a post here and there (and all of them using the same email addy and IP, BTW), etc."
ty sir, you just answered a butload there, makes all the sense in the world now.
btw, i thought it was larry's kid once...
Re: Royal Airforce contact me about John
I admit that I don't use usenet but ummm Wheres the money? Here? With the JT swag? I have never gotten any JT spam?..Where is this money to be made? Can hours upon hours of text be translated into a decent 90 minute movie? Where can I get my JT action figure with distortion unit and chevy?
The Book The Book...Can I buy that book at hastings yet? What about Barnes and Noble? Bookstop? Is Amazon the only place where I can buy it?
Do you think Larry Cluck might sue the JT foundation for copyright infringment or do you think its the other way around, that the JT foundation might sue Larry Cluck for copyright infringement?
Questions Questions....Its all about the money. Millions and Millions of dollars to be made off something only a select fringe minority believe..A select fringe minority that already understands that the story is free online. Hmmmm...Good marketing there. Put everything out free on the net dedicateing days and days to the work and then later put a limited amount of said information in a book and sell it. WE'LL MAKE GAGEILLIANS OF DOLLARS! True marketing genius.
How do this entertainment wizards come up with these ideas!?
I admit that I don't use usenet but ummm Wheres the money? Here? With the JT swag? I have never gotten any JT spam?..Where is this money to be made? Can hours upon hours of text be translated into a decent 90 minute movie? Where can I get my JT action figure with distortion unit and chevy?
The Book The Book...Can I buy that book at hastings yet? What about Barnes and Noble? Bookstop? Is Amazon the only place where I can buy it?
Do you think Larry Cluck might sue the JT foundation for copyright infringment or do you think its the other way around, that the JT foundation might sue Larry Cluck for copyright infringement?
Questions Questions....Its all about the money. Millions and Millions of dollars to be made off something only a select fringe minority believe..A select fringe minority that already understands that the story is free online. Hmmmm...Good marketing there. Put everything out free on the net dedicateing days and days to the work and then later put a limited amount of said information in a book and sell it. WE'LL MAKE GAGEILLIANS OF DOLLARS! True marketing genius.
How do this entertainment wizards come up with these ideas!?
Re: .
Reeling in the Years, stowing away the time (well, that's it for that song from Steely Dan also for the words right now.)
If anyone is interested, there are 24,915 *.pdf files about black holes at the science place. But just to mention a couple, and the rest I kind of forgot, but I was looking for a name I can not remember, nor did I run across it.
It seems like Max Tegmark (I think that is his name)( and all these papers are from June, July this year -- changed versions or corrected there) stated in his paper that we all might as well get use to parallel universes. Let me see here:
arXiv:0704.3276v1 [
hep-th] 24 Apr 2007 (111 pages) Frank Tipler pdf file (version 1)(updated)
arXiv:gr-qc/0701024v3 7 Jun 2007 Prof.Ori's paper (the time machine guy or whatever he is doing.)
And I cannot find Tegmark's paper, but anyone can do a search on "black holes" on the other search, and come up with 24,915 papers in the general field of physics just on black holes. A lot of them -- out in space -- big -- but this year.
I may look at some others again with the search, but there are a lot of them, and I made it through a 1000-1100 of them but I was looking for something else and just rifling through.
Of course that includes every year in that search.
I am tired, and just conclude those papers must include every theory in the Universe somehow, but factual - - not really known yet because the LHC is not on-line yet.
It seems those scientists just write papers because they have to (in a sense - keeping up with the competitiveness type social endeavors.)
Reeling in the Years, stowing away the time (well, that's it for that song from Steely Dan also for the words right now.)
If anyone is interested, there are 24,915 *.pdf files about black holes at the science place. But just to mention a couple, and the rest I kind of forgot, but I was looking for a name I can not remember, nor did I run across it.
It seems like Max Tegmark (I think that is his name)( and all these papers are from June, July this year -- changed versions or corrected there) stated in his paper that we all might as well get use to parallel universes. Let me see here:
arXiv:0704.3276v1 [
hep-th] 24 Apr 2007 (111 pages) Frank Tipler pdf file (version 1)(updated)
arXiv:gr-qc/0701024v3 7 Jun 2007 Prof.Ori's paper (the time machine guy or whatever he is doing.)
And I cannot find Tegmark's paper, but anyone can do a search on "black holes" on the other search, and come up with 24,915 papers in the general field of physics just on black holes. A lot of them -- out in space -- big -- but this year.
I may look at some others again with the search, but there are a lot of them, and I made it through a 1000-1100 of them but I was looking for something else and just rifling through.
Of course that includes every year in that search.
I am tired, and just conclude those papers must include every theory in the Universe somehow, but factual - - not really known yet because the LHC is not on-line yet.
It seems those scientists just write papers because they have to (in a sense - keeping up with the competitiveness type social endeavors.)
Re: .
You know stephen hawking has a myspace... http://profile.myspace.com/index.cfm?fuseaction=user.viewprofile&friendid=61568575&MyToken=450e4724-99f6-46f8-9596-41ce1456b4f8
He's also fairly easy about adding folks...and yea it really is stephen hawking. Just look around on his space and you'll see...but as a wise man "I am not to concerned with who is lying to me online"
You know stephen hawking has a myspace... http://profile.myspace.com/index.cfm?fuseaction=user.viewprofile&friendid=61568575&MyToken=450e4724-99f6-46f8-9596-41ce1456b4f8
He's also fairly easy about adding folks...and yea it really is stephen hawking. Just look around on his space and you'll see...but as a wise man "I am not to concerned with who is lying to me online"
Re: .
Well, if Stephan Hawking has a Myspace page then I bet he is deleting all the spam sign-ups that continue to send to everyone and all those girls who are from China. I deleted my account, as I am tired of it for the last three months until they are found and taken off by Myspace.
What a Zoo!
Feynman-Weinberg Quantum Gravity and the Extended
Standard Model as a Theory of Everything
F. J. Tipler
Department of Mathematics and Department of Physics,
Tulane University, New Orleans, LA 70118
(Dated: April 24, 2007)
Abstract
I argue that the (extended) Standard Model (SM) of particle physics and the renormalizable
Feynman-Weinberg theory of quantum gravity comprise a theory of everything. I show that imposing
the appropriate cosmological boundary conditions make the theory finite. The infinities that
are normally renormalized away and the series divergence infinities are both eliminated by the same
mechanism. Furthermore, this theory can resolve the horizon, flatness, and isotropy problems of
cosmology. Joint mathematical consistency naturally yields a scale-free, Gaussian, adiabatic perturbation
spectrum, and more matter than antimatter. I show that mathematical consistency
of the theory requires the universe to begin at an initial singularity with a pure SU(2)L gauge
field. I show that quantum mechanics requires this field to have a Planckian spectrum whatever
its temperature. If this field has managed to survive thermalization to the present day, then it
would be the CMBR. If so, then we would have a natural explanation for the dark matter and
the dark energy. I show that isotropic ultrahigh energy (UHE) cosmic rays are explained if the
CMBR is a pure SU(2)L gauge field. The SU(2)L nature of the CMBR may have been seen in the
Sunyaev-Zel'dovich effect. I propose several simple experiments to test the hypothesis.
arXiv:0705.0351v4 [gr-qc] 12 Jul 2007
A unified, purely affine theory of gravitation and electromagnetism
Nikodem J. Pop lawski
Department of Physics, Indiana University, 727 East Third Street, Bloomington, Indiana 47405, USA
(Dated: July 12, 2007)
In the purely affine formulation of gravity, the gravitational field is represented by the symmetric
part of the Ricci tensor of the affine connection. The classical electromagnetic field can be rep-
resented in this formulation by the second Ricci tensor of the connection. Such a construction is
dynamically equivalent to the sourceless Einstein–Maxwell equations. We generalize this construc-
tion to the case with sources, represented by the derivative of the affine Lagrangian density with
respect to the connection. We show that the Maxwell equations with sources emerge for the simplest
affine Lagrangian for matter, while the Einstein and Lorentz equations arise if mass has electromag-
netic origin. We also show that the Maxwell equations replace the unphysical constraint imposed
by the projective invariance of purely affine Lagrangians that depend explicitly on the connection.
PACS numbers: 04.50.+h, 04.20.Fy, 03.50.-z
arXiv:0706.3359v1 [hep-th] 22 Jun 2007
Three-Dimensional Gravity Reconsidered
Edward Witten
School of Natural Sciences, Institute for Advanced Study
Princeton, New Jersey 08540
We consider the problem of identifying the CFT’s that may be dual to pure gravity in
three dimensions with negative cosmological constant. The c-theorem indicates that threedimensional
pure gravity is consistent only at certain values of the coupling constant, and
the relation to Chern-Simons gauge theory hints that these may be the values at which
the dual CFT can be holomorphically factorized. If so, and one takes at face value the
minimum mass of a BTZ black hole, then the energy spectrum of three-dimensional gravity
with negative cosmological constant can be determined exactly. At the most negative
possible value of the cosmological constant, the dual CFT is very likely the monster theory
of Frenkel, Lepowsky, and Meurman. The monster theory may be the first in a discrete
series of CFT’s that are dual to three-dimensional gravity. The partition function of the
second theory in the sequence can be determined on a hyperelliptic Riemann surface of
any genus. We also make a similar analysis of supergravity.
arXiv:0707.2593v1 [quant-ph] 18 Jul 2007
Many lives in many worlds
Max Tegmark
(In this universe
Dept. of Physics & MIT Kavli Institute,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
(Dated: Published in Nature, 448, 23, July 2007)
I argue that accepting quantum mechanics to be universally true means that you should also
believe in parallel universes. I give my assessment of Everett’s theory as it celebrates its 50th
anniversary.
Almost all of my colleagues have an opinion about it,
but almost none of them have read it. The first draft of
Hugh Everett’s PhD thesis, the shortened official version
of which celebrates its 50th birthday this year, is buried
in the out-of-print book The Many-Worlds Interpretation
of Quantum Mechanics [1]. I remember my excitement
on finding it in a small Berkeley book store back in grad
school, and still view it as one of the most brilliant texts
I’ve ever read.
By the time Everett started his graduate work with
John Archibald Wheeler at Princeton University, quantum
mechanics had chalked up stunning successes in explaining
the atomic realm, yet a debate raged on as to
what its mathematical formalism really meant. I was fortunate
to get to discuss quantum mechanics withWheeler
during my postdoctorate years in Princeton, but never
had the chance to meet Everett
Perhaps an older paper updated for the Nature Magazine Article, I guess?
There is more, but all that can be looked up.
/ttiforum/images/graemlins/cry.gif
Well, if Stephan Hawking has a Myspace page then I bet he is deleting all the spam sign-ups that continue to send to everyone and all those girls who are from China. I deleted my account, as I am tired of it for the last three months until they are found and taken off by Myspace.
What a Zoo!
Feynman-Weinberg Quantum Gravity and the Extended
Standard Model as a Theory of Everything
F. J. Tipler
Department of Mathematics and Department of Physics,
Tulane University, New Orleans, LA 70118
(Dated: April 24, 2007)
Abstract
I argue that the (extended) Standard Model (SM) of particle physics and the renormalizable
Feynman-Weinberg theory of quantum gravity comprise a theory of everything. I show that imposing
the appropriate cosmological boundary conditions make the theory finite. The infinities that
are normally renormalized away and the series divergence infinities are both eliminated by the same
mechanism. Furthermore, this theory can resolve the horizon, flatness, and isotropy problems of
cosmology. Joint mathematical consistency naturally yields a scale-free, Gaussian, adiabatic perturbation
spectrum, and more matter than antimatter. I show that mathematical consistency
of the theory requires the universe to begin at an initial singularity with a pure SU(2)L gauge
field. I show that quantum mechanics requires this field to have a Planckian spectrum whatever
its temperature. If this field has managed to survive thermalization to the present day, then it
would be the CMBR. If so, then we would have a natural explanation for the dark matter and
the dark energy. I show that isotropic ultrahigh energy (UHE) cosmic rays are explained if the
CMBR is a pure SU(2)L gauge field. The SU(2)L nature of the CMBR may have been seen in the
Sunyaev-Zel'dovich effect. I propose several simple experiments to test the hypothesis.
arXiv:0705.0351v4 [gr-qc] 12 Jul 2007
A unified, purely affine theory of gravitation and electromagnetism
Nikodem J. Pop lawski
Department of Physics, Indiana University, 727 East Third Street, Bloomington, Indiana 47405, USA
(Dated: July 12, 2007)
In the purely affine formulation of gravity, the gravitational field is represented by the symmetric
part of the Ricci tensor of the affine connection. The classical electromagnetic field can be rep-
resented in this formulation by the second Ricci tensor of the connection. Such a construction is
dynamically equivalent to the sourceless Einstein–Maxwell equations. We generalize this construc-
tion to the case with sources, represented by the derivative of the affine Lagrangian density with
respect to the connection. We show that the Maxwell equations with sources emerge for the simplest
affine Lagrangian for matter, while the Einstein and Lorentz equations arise if mass has electromag-
netic origin. We also show that the Maxwell equations replace the unphysical constraint imposed
by the projective invariance of purely affine Lagrangians that depend explicitly on the connection.
PACS numbers: 04.50.+h, 04.20.Fy, 03.50.-z
arXiv:0706.3359v1 [hep-th] 22 Jun 2007
Three-Dimensional Gravity Reconsidered
Edward Witten
School of Natural Sciences, Institute for Advanced Study
Princeton, New Jersey 08540
We consider the problem of identifying the CFT’s that may be dual to pure gravity in
three dimensions with negative cosmological constant. The c-theorem indicates that threedimensional
pure gravity is consistent only at certain values of the coupling constant, and
the relation to Chern-Simons gauge theory hints that these may be the values at which
the dual CFT can be holomorphically factorized. If so, and one takes at face value the
minimum mass of a BTZ black hole, then the energy spectrum of three-dimensional gravity
with negative cosmological constant can be determined exactly. At the most negative
possible value of the cosmological constant, the dual CFT is very likely the monster theory
of Frenkel, Lepowsky, and Meurman. The monster theory may be the first in a discrete
series of CFT’s that are dual to three-dimensional gravity. The partition function of the
second theory in the sequence can be determined on a hyperelliptic Riemann surface of
any genus. We also make a similar analysis of supergravity.
arXiv:0707.2593v1 [quant-ph] 18 Jul 2007
Many lives in many worlds
Max Tegmark
(In this universe
Dept. of Physics & MIT Kavli Institute,Massachusetts Institute of Technology, Cambridge, MA 02139, USA
(Dated: Published in Nature, 448, 23, July 2007)
I argue that accepting quantum mechanics to be universally true means that you should also
believe in parallel universes. I give my assessment of Everett’s theory as it celebrates its 50th
anniversary.
Almost all of my colleagues have an opinion about it,
but almost none of them have read it. The first draft of
Hugh Everett’s PhD thesis, the shortened official version
of which celebrates its 50th birthday this year, is buried
in the out-of-print book The Many-Worlds Interpretation
of Quantum Mechanics [1]. I remember my excitement
on finding it in a small Berkeley book store back in grad
school, and still view it as one of the most brilliant texts
I’ve ever read.
By the time Everett started his graduate work with
John Archibald Wheeler at Princeton University, quantum
mechanics had chalked up stunning successes in explaining
the atomic realm, yet a debate raged on as to
what its mathematical formalism really meant. I was fortunate
to get to discuss quantum mechanics withWheeler
during my postdoctorate years in Princeton, but never
had the chance to meet Everett
Perhaps an older paper updated for the Nature Magazine Article, I guess?
There is more, but all that can be looked up.
/ttiforum/images/graemlins/cry.gif
Re: .
I don't know who all the chics are but when I'm a 65 year old man I hope I have that many chics on Myspace...Two of those guys you see on his friends list..One is his current intern...(edit may of been wrong about top guy) [further edits].. ..But Hey its your business..those blogs of his are heavy in the science of singularities.
Here let me offer you ONE of his blogs.
Rotation, nut charge and anti de sitter space
Black Hole Entropy
The idea is that the Euclidean sections of black hole metrics are periodic in the imaginary time coordinate. Thus they represent black holes in equilibrium with thermal radiation. However there are problems with this interpretation.
Problems with thermodynamic interpretation
(first problem appear)
First, one can not have thermal radiation in asymptotically flat space, all the way to infinity, because the energy density would curve the space, and make it an expanding or collapsing Friedmann universe. Thus, if you want a static situation, you have to resort to the dubious Gedanken experiment, of putting the black hole in a box. But you don't find black hole proof boxes, advertised on the Internet.
(second problem appear)
The second difficulty with black holes in equilibrium with thermal radiation is that black holes have negative specific heat. In many cases, when they absorb energy, they get larger and colder. This reduces the radiation they give off, and so they absorb faster than they radiate, and the equilibrium is unstable. This is closely related to the fact that the Euclidean metric has a negative mode. Thus it seems that asymptotically flat Euclidean black holes, describe the decay of hot flat space, rather than a black hole in equilibrium with thermal radiation.
(third problem appear)
The third difficulty with the idea of equilibrium is that if the black hole is rotating, the thermal radiation should be co-rotating with it. But far away from the black hole, the radiation would be co-rotating faster than light, which is impossible. Thus, again one has to use the artificial expedient, of a box of finite size.
Way back in pre-history, Don page and I, realized one could avoid the first two difficulties, if one considered black holes in anti de Sitter space, rather than asymptotically-flat space. In anti de Sitter space, the gravitational potential increases as one goes to infinity. This red shifts the thermal radiation, and means that it has finite energy. Thus anti de Sitter space can exist at finite temperature, without collapsing. In a sense, the gravitational potential in anti de Sitter space, acts like a confining box.
Anti de Sitter space can also help with the second problem, that the equilibrium between black holes and thermal radiation, will be unstable. Small black holes in anti de Sitter space, have negative specific heat, like in asymptotically flat space, and are unstable. But black holes larger than the curvature radius of anti de Sitter space, have positive specific heat, and are presumably stable.
At the time, Don page and I, did not think about rotating black holes. But I recently came back to the problem, along with Chris Hunter, and Marika Taylor Robinson. We realized that thermal radiation in anti de Sitter space could co-rotate with up to some limiting angular velocity, without having to travel faster than light. Thus anti de Sitter boundary conditions, can solve all three problems, in the interpretation of Euclidean black holes, as equilibria of black holes, with thermal radiation.
Anti de Sitter black holes may not seem of much interest, because we can be fairly sure, that the universe is not asymptotically anti de Sitter. However, they seem worth studying, both for the reasons I have just given, and because of the Maldacena conjecture, relating asymptotically anti de Sitter spaces, to conformal field theories on their boundary. I shall report on two pieces of work in relation to this conjecture. One is a study of rotating black holes in anti de Sitter space. We have found Kerr anti de Sitter metrics in four and five dimensions. As they approach the critical angular velocity in anti de Sitter space, their entropy, as measured by the horizon area, diverges. We compare this entropy, with that of a conformal field theory on the boundary of anti de Sitter space. This also diverges at the critical angular velocity, when the rotational velocity, approaches the speed of light. We show that the two divergences are similar.
The other piece of work, is a study of gravitational entropy, in a more general setting. The quarter area law, holds for black holes or black branes in any dimension, d, that have a horizon, which is a d minus 2 dimensional fixed point set, of a U1 isometry group. However Chris Hunter and I, have recently shown that entropy can be associated with a more general class of space-times. In these, the U1 isometry group can have fixed points on surfaces of any even co-dimension, and the space-time need not be asymptotically flat, or asymptotically anti de Sitter. In these more general class, the entropy is not just a quarter the area, of the d minus two fixed point set.
Among the more general class of space-times for which entropy can be defined, an interesting case is those with Nut charge. Nut charge can be defined in four dimensions, and can be regarded as a magnetic type of mass.
Solutions with nut charge are not asymptotically flat in the usual sense. Instead, they are said to be asymptotically locally flat, or ALF. In the Euclidean regime, in which I shall be working, the difference can be described as follows. An asymptotically flat metric, like Euclidean Schwarzschild, has a boundary at infinity, that is a two-sphere of radius r, cross a circle, whose radius is asymptotically constant.
To get finite values for the action and Hamiltonian, one subtracts the values for flat space, periodically identified. In asymptotically locally flat metrics, on the other hand, the boundary at infinity, is an S1 bundle over S2. These bundles are labeled by their first Chern number, which is proportional to the Nut charge. If the first Chern number is zero, the boundary is the product, S2 cross S1, and the metric is asymptotically flat. However, if the first Chern number is k, the boundary is a squashed three sphere, with mod k points identified around the S1 fibers.
Such asymptotically locally flat metrics, can not be matched to flat space at infinity, to give a finite action and Hamiltonian, despite a number of papers that claim it can be done. The best that one can do, is match to the self-dual multi Taub nut solutions. These can be regarded as defining the vacuums for ALF metrics.
In the self-dual Taub Nut solution, the U1 isometry group, has a zero dimensional fixed point set at the center, called a nut. However, the same ALF boundary conditions, admit another Euclidean solution, called the Taub bolt metric, in which the nut is replaced by a two dimensional bolt. The interesting feature, is that according to the new definition of entropy, the entropy of Taub bolt, is not equal to a quarter the area of the bolt, in Planck units. The reason is that there is a contribution to the entropy from the Misner string, the gravitational counterpart to a Dirac string for a gauge field.
The fact that black hole entropy is proportional to the area of the horizon has led people to try and identify the microstates, with states on the horizon. After years of failure, success seemed to come in 1996, with the paper of Strominger and Vafa, which connected the entropy of certain black holes, with a system of D-branes. With hindsight, this can now be seen as an example of a duality, between a gravitational theory in asymptotically anti de Sitter space, and a conformal field theory on its boundary.
It would be interesting if similar dualities could be found for solutions with Nut charge, so that one could verify that the contribution of the Misner string was reflected in the entropy of a conformal field theory. This would be particularly significant for solutions like Taub bolt, which don't have a spin structure. It would show whether the duality between anti de Sitter space, and conformal field theories on its boundary, depends on super symmetry. In fact, I will present evidence, that the duality requires super symmetry.
To investigate the effect of Nut charge, we have found a family of Taub bolt anti de Sitter solutions. These Euclidean metrics are characterized by an integer, k, and a positive parameter, s. The boundary at large distances is an S1 bundle over S2, with first Chern number, k. If k=0, the boundary is a product, S1 cross S2, and the space is asymptotically anti de Sitter, in the usual sense. But if k is not zero, they are what may be called, asymptotically locally anti de Sitter, or ALADS.
The boundary is a squashed three sphere, with k points identified around the U1 direction. This is just like asymptotically locally flat, or ALF metrics. But unlike the ALF case, the squashing of the three-sphere, tends to a finite limit, as one approaches infinity. This means that the boundary has a well-defined conformal structure. One can then ask whether the partition function and entropy, of a conformal field theory on the boundary, is related to the action and entropy, of these asymptotically locally anti de Sitter solutions.
To make the ADS, CFT correspondence well posed, we have to specify the reference backgrounds, with respect to which the actions and Hamiltonians are defined. For Kerr anti de Sitter, the reference background is just identified anti de Sitter space. However, as in the asymptotically locally flat case, a squashed three sphere, can not be imbedded in Euclidean anti de Sitter. One therefore can not use it as a reference background, to make the action and Hamiltonian finite.
Instead, one has to use Taub Nut anti de Sitter, which is a limiting case of our family. If mod k is greater than one, there is an orbifold singularity in the reference backgrounds, but not in the Taub bolt anti de Sitter solutions. These orbifold singularities in the backgrounds could be resolved, by replacing a small neighbourhood of the nut, by an ALE metric. We shall take it, that the orbifold singularities are harmless.
Another issue that has to be resolved, is what conformal field theory to use, on the boundary of the anti de Sitter space. For five dimensional Kerr anti de Sitter space, there are good reasons to believe the boundary theory is large N Yang Mills. But for four-dimensional Kerr anti de Sitter, or Taub bolt anti de Sitter, we are on shakier ground. On the three dimensional boundaries of four dimensional anti de Sitter spaces, Yang Mills theory is not conformally invariant.
The folklore is that one takes the infrared fixed point, of three-dimensional Yang Mills, but no one knows what this is. The best we can do, is calculate the determinants of free fields on the squashed three sphere, and see if they have the same dependence on the squashing, as the action. Note that as the boundary is odd dimensional, there is no conformal anomaly. The determinant of a conformally invariant operator, will just be a function of the squashing. We can then interpret the squashing, as the inverse temperature, and get the number of degrees of freedom, from a comparison with the entropy of ordinary black holes, in four dimensional anti de Sitter.
I now turn to the question, of how one can define the entropy, of a space-time. A thermodynamic ensemble, is a collection of systems, whose charges are constrained by La-grange multipliers.
Partition function
One such charge, is the energy or mass, with the Lagrange multiplier being the inverse temperature, beta. But one can also constrain the angular momentum, and gauge charges. The partition function for the ensemble, is the sum over all states, of e to the minus, La-grange multipliers, times associated charges.
Thus it can be written as, trace of e to the minus Q. Here Q is the operator that generates a Euclidean time translation, beta, a rotation, delta phi, and a gauge transformation, alpha. In other words, Q is the Hamiltonian operator, for a lapse that is beta at infinity, and a shift that is a rotation through delta phi. This means that the partition function can be represented by a Euclidean path integral.
The path integral is over all metrics which at infinity, are periodic under the combination of a Euclidean time translation, beta, a rotation through delta phi, and a gauge rotation, alpha. The lowest order contributions to the path integral for the partition function will come from Euclidean solutions with a U1 isometry, that agree with the periodic boundary conditions at infinity.
The Hamiltonian in general relativity or supergravity, can be written as a volume integral over a surface of constant tau, plus surface integrals over its boundaries.
Gravitational Hamiltonian
The volume integral vanishes by the constraint equations. Thus the numerical value of the Hamiltonian, comes entirely from the surface terms. The action can be related to the Hamiltonian in the usual way.
Because the metric has a time translation isometry, all dotted quantities vanish. Thus the action is just beta times the Hamiltonian.
If the solution can be foliated by a family of surfaces, that agree with Euclidean time at infinity, the only surface terms will be at infinity.
Family of time surfaces
In this case, a solution can be identified under any time translation, rotation, or gauge transformation at infinity.
This means that the action will be linear in beta, delta phi, and alpha. If one takes such a linear action, for the partition function, and applies the standard thermodynamic relations, one finds the entropy is zero.
The situation is very different however, if the solution can't be foliated by surfaces of constant tau, where tau is the parameter of the U1 isometry group, which agrees with the periodic identification at infinity.
Breakdown of foliation
The break down of foliation can occur in two ways. The first is at fixed points of the U1 isometry group. These occur on surfaces of even co-dimension. Fixed-point sets of co-dimension-two play a special role. I shall refer to them as bolts. Examples include the horizons of non-extreme black holes and p-branes, but there can be more complicated cases, like Taub bolt.
The other way the foliation by surfaces of constant tau, can break down, is if there are what are called, Misner strings.
Kaluza Klein metric
To explain what they are, write the metric in the Kaluza Klein form, with respect to the U1 isometry group. The one form, omega, the scalar, V, and the metric, gamma, can be regarded as fields on B, the space of orbits of the isometry group.
If B has homology in dimension two, the Kaluza Klein field strength, F, can have non-zero integrals over two cycles. This means that the one form, omega, will have Dirac strings in B. In turn, this will mean that the foliation of the spacetime, M, by surfaces of constant tau, will break down on surfaces of co-dimension two, called Misner strings.
In order to do a Hamiltonian treatment using surfaces of constant tau, one has to cut out small neighbourhoods of the fixed point sets, and the Misner strings. This modifies the treatment, in two ways. First, the surfaces of constant tau now have boundaries at the fixed-point sets, and Misner strings, as well as the boundary at infinity. This means there can be additional surface terms in the Hamiltonian.
In fact, the surface terms at the fixed-point sets are zero, because the shift and lapse vanish there. On the other hand, at a Misner string, the lapse vanishes, but the shift is non zero. The Hamiltonian can therefore have a surface term on the Misner string, which is the shift, times a component of the second fundamental form, of the constant tau surfaces. The total Hamiltonian, will be the sum of this Misner string Hamiltonian, and the Hamiltonian surface term at infinity.
Consequences of non-foliation
As before, the action will be beta times the Hamiltonian. However, this will be the action of the space-time, with the neighborhoods of the fixed-point sets and Misner strings removed. To get the action of the full space-time, one has to put back the neighborhoods. When one does so, the surface term associated with the Einstein Hilbert action, will give a contribution to the action, of minus area over 4G, for the bolts and Misner strings. Here G is Newton's constant in the dimension one is considering. The surface terms around lower dimensional fixed-point sets make no contribution to the action.
The action of the space-time, will be the lowest order contribution to minus log Z, where Z is the partition function. But log Z is equal to the entropy, minus beta times the Hamiltonian at infinity. So the entropy is a quarter the area of the bolts and Misner strings, minus beta times the Hamiltonian on the Misner strings. In other words, the entropy is the amount by which the action is less than the value, beta times the Hamiltonian at infinity, that it would have if the surfaces of constant tau, foliated the space-time.
This formula for the entropy applies in any dimension and for any class of boundary condition at infinity. Thus one can use it for rotating black holes, in anti de Sitter space. In this case, the reference background is just Euclidean anti de Sitter space, identified with imaginary time period, beta, and appropriate rotation.
Four-dimensional Kerr-AdS
The four-dimensional Kerr anti de Sitter solution, was found by Carter, and is shown on the slide. The parameter, a, determines the rate of rotation. When a-l approaches 1, the co-rotation velocity approaches the speed of light at infinity. It is therefore interesting to examine the behavior of the black hole action, and the conformal field theory partition function, in this limit.
To calculate the action of the black hole is quite delicate, because one has to match it to rotating anti de Sitter space, and subtract one infinite quantity, from another.
Euclidean action.
Nevertheless, this can be done in a well-defined way, and the result is shown on the slide. As you might expect, it diverges at the critical angular velocity, at which the co-rotating velocity, approaches the speed of light.
The boundary of rotating anti de Sitter, is a rotating Einstein universe, of one dimension lower. Thus it is straightforward in principle, to calculate the partition function for a free conformal field on the boundary. Someone like Dowker might have calculated the result exactly. However, as we are only human, we looked only at the divergence in the partition function, as one approaches the critical angular velocity.
This divergence arises because in the mode sum for the partition function, one has Bose-Einstein factors with a correction because of the rotation. As one approaches the critical angular velocity, this causes a Bose-Einstein condensation in modes with the maximum axial quantum number, m.
Conformal field theory
The divergence in the conformal field theory partition function has the same divergence as the black hole action, at the critical angular velocity. I haven't compared the residues. This is difficult, because it is not clear what three-dimensional conformal field theory one should use on the boundary of four dimensional anti de Sitter.
Five-dimensional Kerr-AdS
The case of rotating black holes in anti de Sitter five, is broadly similar, but with some differences. One of these is that, because the spatial rotation group, O4, is of rank 2, there are two rotation parameters, a & b. Each of these must have absolute value less than l to the minus one, for the co-rotation velocity to be less than the speed of light, all the way out to infinity. If just one of a & b, approaches the limiting value, the action of the black hole, and the partition function of the conformal field theory, both diverge in a manner similar to the four dimensional case.
Action of five-dimensional Kerr-AdS
But if a = b, and they approach the limit together, the action and the partition function, both have the same stronger divergence. Again, I haven't compared residues, but this might be worth doing. It may be that in the critical angular velocity limit, the interactions between the particles of super Yang Mills theory, become unimportant. If this is the case, one would expect the action and partition function to agree, rather than differ by a factor of four thirds, as in the non rotating case.
Asymptotically locally flat
I now turn the case of Nut charge. For asymptotically locally flat metrics in four dimensions, the reference background is the self-dual Taub Nut solution. The Taub bolt solution, has the same asymptotic behavior, but with the zero-dimensional nut fixed point, replaced by a two-dimensional bolt. The area of the bolt is 12 pi N squared, where N is the Nut charge. The area of the Misner string is minus 6 pi N squared. That is to say, the area of the Misner string in Taub bolt, is infinite, but it is less than the area of the Misner string in Taub nut, in a well-defined sense. The Hamiltonian on the Misner string, is N over 8. Again the Misner string Hamiltonian is infinite, but the difference from Taub nut, is finite. And the period, beta, is 8pi N. Thus the entropy, is pi N squared. Note that this is less than a quarter the area of the bolt, which would give 3 pi N squared. It is the effect of the Misner string that reduces the entropy.
Taub Nut Anti de Sitter
We would like to confirm the effect of Misner strings on entropy, by seeing what effect they have on conformal field theories, on the boundary of anti de Sitter space. For this purpose we constructed versions of Taub nut and Taub bolt, with a negative cosmological constant. The Taub nut anti de Sitter metric is shown on the transparancy. The parameter E, is the squashing of the three-sphere at infinity. If E=1, the three spheres are round, and the metric is Euclidean anti de Sitter space. However, if E is not equal to one, the metric can not be matched to anti de Sitter space at large distance. Each value of E, therefore, defines a different sector of ALADS metrics. This is an important point, which did not seem to have been realized by Chamblin et al. Taub Bolt Anti de Sitter One can also find a family of Taub bolt anti de Sitter metrics, with the same asymptotic behavior. These are characterized by an integer, k, and a positive quantity, s. These determine the asymptotic squashing parameter, E, and the area of the bolt, A-. K is the self-intersection number of the bolt. Thus the spaces do not have spin structure if k is odd. At infinity, the squashed three sphere has k points identified around the U1 fiber. This means that the reference background, is Taub nut anti de Sitter, with k points identified. If k is greater than one, the reference background will have an orbifold singularity at the nut. However, as I said earlier, I shall take it that such singularities are harmless.
Action
To calculate the action, one matches the Taub bolt solution on a squashed three sphere, to a Taub nut solution. To do this, one has to re-scale the squashing parameter, E, as a function of radius. The surface term in the action, is the same asymptotically for Taub nut and Taub bolt. Thus the action comes entirely from the difference in volumes.
Action for k = 1
For k greater than one, the action is always negative, while for k=1, it is positive for small areas of the bolt, and negative for large areas. This behavior is similar to that for Schwarzschild anti de Sitter space, and might indicate a phase transition in the corresponding conformal field theory. However, as I will argue later, there are problems with the ADS, CFT duality, if k=1. On the other hand, our results seem to indicate that there will be no phase transition, if more than one point is identified around the fiber. It will be interesting to see if this is indeed the case, for a conformal field theory on an identified squashed three-sphere.
In these Taub bolt anti de Sitter metrics, one can calculate the area of the Misner string, and the Hamiltonian surface term. Both will be infinite, but if one matches to Taub nut anti de Sitter on a large squashed three-sphere, the differences will tend to finite limits. As in the asymptotically locally flat case, the entropy is less than a quarter the area of the bolt, because of the effect of the Misner string.
Entropy
One can also calculate the entropy from the partition function, by the usual thermodynamic relations. The mass will be given by taking the derivative of the action with respect to beta. This is equal to the Hamiltonian surface term at infinity. The mass or energy, is the only charge that is constrained in the ensemble. The nut charge is fixed by the boundary conditions, and so doesn't need a La-grange multiplier. Thus the entropy is beta M, minus I. This agrees with the entropy calculated from the bolts and Misner strings, showing our definition, is consistent.
Formally at least, one can regard Euclidean conformal field theory on the squashed three sphere, as a twisted 2+1 theory, at a temperature, beta to the minus one. Thus one would expect the entropy to be proportional to beta to the minus two, at least for small beta. This has been confirmed by calculations by Dowker, of the determinants of scalar and fermion operators on the squashed three sphere, for k=1.
Dowker has not so far calculated the higher k cases, but one would expect that these would have similar leading terms, but with beta replaced by beta over k. The next leading order terms in the determinant, are beta to the minus one, log beta. No terms like this appear in the bulk theory, so if there really is an ADS, CFT duality in this situation, the log beta terms have to cancel between the different spins.
In fact, the scalar and fermion log beta terms will cancel each other, if there are twice as many scalars as fermions. This would be implied by super symmetry, suggesting that super symmetry is indeed necessary for the ADS, CFT duality.
The Misner string contributions to the entropy are of order beta squared. Thus Dowker's calculations will have to be extended to this order, to k greater than one, to fermion fields with anti periodic boundary conditions, and to spin one fields. All this is quite possible, but it will probably require Dowker to do it.
One might ask, how can a conformal field theory on the Euclidean squashed three sphere, correspond to a theory in a spacetime of Lorentzian signature. The answer is that, unlike the Schwarzschild anti de Sitter case, one has to continue the period, beta, to imaginary values. This makes the spacetime periodic in real time, rather than imaginary time. One gets a 2+1 rotating spacetime, rather like the Goedel universe, with closed time like curves. Although field theory in such a spacetime, may seem pathological, it can be obtained by analytical continuation, and is well defined despite the lack of causality. It is interesting that the analytically continued entropy, is negative, suggesting that causality violating spacetimes, are quantum suppressed. However, it is probably a mistake, to attach physical significance, to the Lorentzian conformal field theory.
To sum up, I discussed the ADS, CFT duality in two new contexts. That of rotating black holes and that of solutions with nut charge. I showed how gravitational entropy can be defined in general. The partition function for a thermodynamic ensemble can be defined by a path integral over periodic metrics. The lowest order contributions to the partition function will come from metrics with a U1 isometry, and given behavior at infinity. The entropy of such metrics will receive contributions from horizons or bolts, and from Misner strings, which are the Dirac strings of the U1 isometry, under Kaluza Klein reduction. One would like to relate this gravitational entropy, to the entropy of a conformal field theory on the boundary. For this reason, we considered a new class of asymptotically locally anti de Sitter spaces. Other people have investigated the Maldacena conjecture, by deforming the compact part of the metric, but this is the first time deformed anti de Sitter boundary conditions, have been considered.
We studied Taub bolt anti de Sitter solutions, with Taub nut anti de Sitter, as the reference background. The entropy we obtained obeyed the right thermodynamic relations, and had the right temperature dependence, to be the entropy of a conformal field theory, on the squashed three sphere. Because the Taub bolt solutions for odd k, do not have spin structures, this may indicate that the anti de Sitter, conformal field theory correspondence, does not depend on super symmetry.
I will end by saying that gravitational entropy, is alive and well, 34 years on. But there's more to entropy, than just horizon area. We need to look at the nuts and bolts.
I don't know who all the chics are but when I'm a 65 year old man I hope I have that many chics on Myspace...Two of those guys you see on his friends list..One is his current intern...(edit may of been wrong about top guy) [further edits].. ..But Hey its your business..those blogs of his are heavy in the science of singularities.
Here let me offer you ONE of his blogs.
Rotation, nut charge and anti de sitter space
Black Hole Entropy
The idea is that the Euclidean sections of black hole metrics are periodic in the imaginary time coordinate. Thus they represent black holes in equilibrium with thermal radiation. However there are problems with this interpretation.
Problems with thermodynamic interpretation
(first problem appear)
First, one can not have thermal radiation in asymptotically flat space, all the way to infinity, because the energy density would curve the space, and make it an expanding or collapsing Friedmann universe. Thus, if you want a static situation, you have to resort to the dubious Gedanken experiment, of putting the black hole in a box. But you don't find black hole proof boxes, advertised on the Internet.
(second problem appear)
The second difficulty with black holes in equilibrium with thermal radiation is that black holes have negative specific heat. In many cases, when they absorb energy, they get larger and colder. This reduces the radiation they give off, and so they absorb faster than they radiate, and the equilibrium is unstable. This is closely related to the fact that the Euclidean metric has a negative mode. Thus it seems that asymptotically flat Euclidean black holes, describe the decay of hot flat space, rather than a black hole in equilibrium with thermal radiation.
(third problem appear)
The third difficulty with the idea of equilibrium is that if the black hole is rotating, the thermal radiation should be co-rotating with it. But far away from the black hole, the radiation would be co-rotating faster than light, which is impossible. Thus, again one has to use the artificial expedient, of a box of finite size.
Way back in pre-history, Don page and I, realized one could avoid the first two difficulties, if one considered black holes in anti de Sitter space, rather than asymptotically-flat space. In anti de Sitter space, the gravitational potential increases as one goes to infinity. This red shifts the thermal radiation, and means that it has finite energy. Thus anti de Sitter space can exist at finite temperature, without collapsing. In a sense, the gravitational potential in anti de Sitter space, acts like a confining box.
Anti de Sitter space can also help with the second problem, that the equilibrium between black holes and thermal radiation, will be unstable. Small black holes in anti de Sitter space, have negative specific heat, like in asymptotically flat space, and are unstable. But black holes larger than the curvature radius of anti de Sitter space, have positive specific heat, and are presumably stable.
At the time, Don page and I, did not think about rotating black holes. But I recently came back to the problem, along with Chris Hunter, and Marika Taylor Robinson. We realized that thermal radiation in anti de Sitter space could co-rotate with up to some limiting angular velocity, without having to travel faster than light. Thus anti de Sitter boundary conditions, can solve all three problems, in the interpretation of Euclidean black holes, as equilibria of black holes, with thermal radiation.
Anti de Sitter black holes may not seem of much interest, because we can be fairly sure, that the universe is not asymptotically anti de Sitter. However, they seem worth studying, both for the reasons I have just given, and because of the Maldacena conjecture, relating asymptotically anti de Sitter spaces, to conformal field theories on their boundary. I shall report on two pieces of work in relation to this conjecture. One is a study of rotating black holes in anti de Sitter space. We have found Kerr anti de Sitter metrics in four and five dimensions. As they approach the critical angular velocity in anti de Sitter space, their entropy, as measured by the horizon area, diverges. We compare this entropy, with that of a conformal field theory on the boundary of anti de Sitter space. This also diverges at the critical angular velocity, when the rotational velocity, approaches the speed of light. We show that the two divergences are similar.
The other piece of work, is a study of gravitational entropy, in a more general setting. The quarter area law, holds for black holes or black branes in any dimension, d, that have a horizon, which is a d minus 2 dimensional fixed point set, of a U1 isometry group. However Chris Hunter and I, have recently shown that entropy can be associated with a more general class of space-times. In these, the U1 isometry group can have fixed points on surfaces of any even co-dimension, and the space-time need not be asymptotically flat, or asymptotically anti de Sitter. In these more general class, the entropy is not just a quarter the area, of the d minus two fixed point set.
Among the more general class of space-times for which entropy can be defined, an interesting case is those with Nut charge. Nut charge can be defined in four dimensions, and can be regarded as a magnetic type of mass.
Solutions with nut charge are not asymptotically flat in the usual sense. Instead, they are said to be asymptotically locally flat, or ALF. In the Euclidean regime, in which I shall be working, the difference can be described as follows. An asymptotically flat metric, like Euclidean Schwarzschild, has a boundary at infinity, that is a two-sphere of radius r, cross a circle, whose radius is asymptotically constant.
To get finite values for the action and Hamiltonian, one subtracts the values for flat space, periodically identified. In asymptotically locally flat metrics, on the other hand, the boundary at infinity, is an S1 bundle over S2. These bundles are labeled by their first Chern number, which is proportional to the Nut charge. If the first Chern number is zero, the boundary is the product, S2 cross S1, and the metric is asymptotically flat. However, if the first Chern number is k, the boundary is a squashed three sphere, with mod k points identified around the S1 fibers.
Such asymptotically locally flat metrics, can not be matched to flat space at infinity, to give a finite action and Hamiltonian, despite a number of papers that claim it can be done. The best that one can do, is match to the self-dual multi Taub nut solutions. These can be regarded as defining the vacuums for ALF metrics.
In the self-dual Taub Nut solution, the U1 isometry group, has a zero dimensional fixed point set at the center, called a nut. However, the same ALF boundary conditions, admit another Euclidean solution, called the Taub bolt metric, in which the nut is replaced by a two dimensional bolt. The interesting feature, is that according to the new definition of entropy, the entropy of Taub bolt, is not equal to a quarter the area of the bolt, in Planck units. The reason is that there is a contribution to the entropy from the Misner string, the gravitational counterpart to a Dirac string for a gauge field.
The fact that black hole entropy is proportional to the area of the horizon has led people to try and identify the microstates, with states on the horizon. After years of failure, success seemed to come in 1996, with the paper of Strominger and Vafa, which connected the entropy of certain black holes, with a system of D-branes. With hindsight, this can now be seen as an example of a duality, between a gravitational theory in asymptotically anti de Sitter space, and a conformal field theory on its boundary.
It would be interesting if similar dualities could be found for solutions with Nut charge, so that one could verify that the contribution of the Misner string was reflected in the entropy of a conformal field theory. This would be particularly significant for solutions like Taub bolt, which don't have a spin structure. It would show whether the duality between anti de Sitter space, and conformal field theories on its boundary, depends on super symmetry. In fact, I will present evidence, that the duality requires super symmetry.
To investigate the effect of Nut charge, we have found a family of Taub bolt anti de Sitter solutions. These Euclidean metrics are characterized by an integer, k, and a positive parameter, s. The boundary at large distances is an S1 bundle over S2, with first Chern number, k. If k=0, the boundary is a product, S1 cross S2, and the space is asymptotically anti de Sitter, in the usual sense. But if k is not zero, they are what may be called, asymptotically locally anti de Sitter, or ALADS.
The boundary is a squashed three sphere, with k points identified around the U1 direction. This is just like asymptotically locally flat, or ALF metrics. But unlike the ALF case, the squashing of the three-sphere, tends to a finite limit, as one approaches infinity. This means that the boundary has a well-defined conformal structure. One can then ask whether the partition function and entropy, of a conformal field theory on the boundary, is related to the action and entropy, of these asymptotically locally anti de Sitter solutions.
To make the ADS, CFT correspondence well posed, we have to specify the reference backgrounds, with respect to which the actions and Hamiltonians are defined. For Kerr anti de Sitter, the reference background is just identified anti de Sitter space. However, as in the asymptotically locally flat case, a squashed three sphere, can not be imbedded in Euclidean anti de Sitter. One therefore can not use it as a reference background, to make the action and Hamiltonian finite.
Instead, one has to use Taub Nut anti de Sitter, which is a limiting case of our family. If mod k is greater than one, there is an orbifold singularity in the reference backgrounds, but not in the Taub bolt anti de Sitter solutions. These orbifold singularities in the backgrounds could be resolved, by replacing a small neighbourhood of the nut, by an ALE metric. We shall take it, that the orbifold singularities are harmless.
Another issue that has to be resolved, is what conformal field theory to use, on the boundary of the anti de Sitter space. For five dimensional Kerr anti de Sitter space, there are good reasons to believe the boundary theory is large N Yang Mills. But for four-dimensional Kerr anti de Sitter, or Taub bolt anti de Sitter, we are on shakier ground. On the three dimensional boundaries of four dimensional anti de Sitter spaces, Yang Mills theory is not conformally invariant.
The folklore is that one takes the infrared fixed point, of three-dimensional Yang Mills, but no one knows what this is. The best we can do, is calculate the determinants of free fields on the squashed three sphere, and see if they have the same dependence on the squashing, as the action. Note that as the boundary is odd dimensional, there is no conformal anomaly. The determinant of a conformally invariant operator, will just be a function of the squashing. We can then interpret the squashing, as the inverse temperature, and get the number of degrees of freedom, from a comparison with the entropy of ordinary black holes, in four dimensional anti de Sitter.
I now turn to the question, of how one can define the entropy, of a space-time. A thermodynamic ensemble, is a collection of systems, whose charges are constrained by La-grange multipliers.
Partition function
One such charge, is the energy or mass, with the Lagrange multiplier being the inverse temperature, beta. But one can also constrain the angular momentum, and gauge charges. The partition function for the ensemble, is the sum over all states, of e to the minus, La-grange multipliers, times associated charges.
Thus it can be written as, trace of e to the minus Q. Here Q is the operator that generates a Euclidean time translation, beta, a rotation, delta phi, and a gauge transformation, alpha. In other words, Q is the Hamiltonian operator, for a lapse that is beta at infinity, and a shift that is a rotation through delta phi. This means that the partition function can be represented by a Euclidean path integral.
The path integral is over all metrics which at infinity, are periodic under the combination of a Euclidean time translation, beta, a rotation through delta phi, and a gauge rotation, alpha. The lowest order contributions to the path integral for the partition function will come from Euclidean solutions with a U1 isometry, that agree with the periodic boundary conditions at infinity.
The Hamiltonian in general relativity or supergravity, can be written as a volume integral over a surface of constant tau, plus surface integrals over its boundaries.
Gravitational Hamiltonian
The volume integral vanishes by the constraint equations. Thus the numerical value of the Hamiltonian, comes entirely from the surface terms. The action can be related to the Hamiltonian in the usual way.
Because the metric has a time translation isometry, all dotted quantities vanish. Thus the action is just beta times the Hamiltonian.
If the solution can be foliated by a family of surfaces, that agree with Euclidean time at infinity, the only surface terms will be at infinity.
Family of time surfaces
In this case, a solution can be identified under any time translation, rotation, or gauge transformation at infinity.
This means that the action will be linear in beta, delta phi, and alpha. If one takes such a linear action, for the partition function, and applies the standard thermodynamic relations, one finds the entropy is zero.
The situation is very different however, if the solution can't be foliated by surfaces of constant tau, where tau is the parameter of the U1 isometry group, which agrees with the periodic identification at infinity.
Breakdown of foliation
The break down of foliation can occur in two ways. The first is at fixed points of the U1 isometry group. These occur on surfaces of even co-dimension. Fixed-point sets of co-dimension-two play a special role. I shall refer to them as bolts. Examples include the horizons of non-extreme black holes and p-branes, but there can be more complicated cases, like Taub bolt.
The other way the foliation by surfaces of constant tau, can break down, is if there are what are called, Misner strings.
Kaluza Klein metric
To explain what they are, write the metric in the Kaluza Klein form, with respect to the U1 isometry group. The one form, omega, the scalar, V, and the metric, gamma, can be regarded as fields on B, the space of orbits of the isometry group.
If B has homology in dimension two, the Kaluza Klein field strength, F, can have non-zero integrals over two cycles. This means that the one form, omega, will have Dirac strings in B. In turn, this will mean that the foliation of the spacetime, M, by surfaces of constant tau, will break down on surfaces of co-dimension two, called Misner strings.
In order to do a Hamiltonian treatment using surfaces of constant tau, one has to cut out small neighbourhoods of the fixed point sets, and the Misner strings. This modifies the treatment, in two ways. First, the surfaces of constant tau now have boundaries at the fixed-point sets, and Misner strings, as well as the boundary at infinity. This means there can be additional surface terms in the Hamiltonian.
In fact, the surface terms at the fixed-point sets are zero, because the shift and lapse vanish there. On the other hand, at a Misner string, the lapse vanishes, but the shift is non zero. The Hamiltonian can therefore have a surface term on the Misner string, which is the shift, times a component of the second fundamental form, of the constant tau surfaces. The total Hamiltonian, will be the sum of this Misner string Hamiltonian, and the Hamiltonian surface term at infinity.
Consequences of non-foliation
As before, the action will be beta times the Hamiltonian. However, this will be the action of the space-time, with the neighborhoods of the fixed-point sets and Misner strings removed. To get the action of the full space-time, one has to put back the neighborhoods. When one does so, the surface term associated with the Einstein Hilbert action, will give a contribution to the action, of minus area over 4G, for the bolts and Misner strings. Here G is Newton's constant in the dimension one is considering. The surface terms around lower dimensional fixed-point sets make no contribution to the action.
The action of the space-time, will be the lowest order contribution to minus log Z, where Z is the partition function. But log Z is equal to the entropy, minus beta times the Hamiltonian at infinity. So the entropy is a quarter the area of the bolts and Misner strings, minus beta times the Hamiltonian on the Misner strings. In other words, the entropy is the amount by which the action is less than the value, beta times the Hamiltonian at infinity, that it would have if the surfaces of constant tau, foliated the space-time.
This formula for the entropy applies in any dimension and for any class of boundary condition at infinity. Thus one can use it for rotating black holes, in anti de Sitter space. In this case, the reference background is just Euclidean anti de Sitter space, identified with imaginary time period, beta, and appropriate rotation.
Four-dimensional Kerr-AdS
The four-dimensional Kerr anti de Sitter solution, was found by Carter, and is shown on the slide. The parameter, a, determines the rate of rotation. When a-l approaches 1, the co-rotation velocity approaches the speed of light at infinity. It is therefore interesting to examine the behavior of the black hole action, and the conformal field theory partition function, in this limit.
To calculate the action of the black hole is quite delicate, because one has to match it to rotating anti de Sitter space, and subtract one infinite quantity, from another.
Euclidean action.
Nevertheless, this can be done in a well-defined way, and the result is shown on the slide. As you might expect, it diverges at the critical angular velocity, at which the co-rotating velocity, approaches the speed of light.
The boundary of rotating anti de Sitter, is a rotating Einstein universe, of one dimension lower. Thus it is straightforward in principle, to calculate the partition function for a free conformal field on the boundary. Someone like Dowker might have calculated the result exactly. However, as we are only human, we looked only at the divergence in the partition function, as one approaches the critical angular velocity.
This divergence arises because in the mode sum for the partition function, one has Bose-Einstein factors with a correction because of the rotation. As one approaches the critical angular velocity, this causes a Bose-Einstein condensation in modes with the maximum axial quantum number, m.
Conformal field theory
The divergence in the conformal field theory partition function has the same divergence as the black hole action, at the critical angular velocity. I haven't compared the residues. This is difficult, because it is not clear what three-dimensional conformal field theory one should use on the boundary of four dimensional anti de Sitter.
Five-dimensional Kerr-AdS
The case of rotating black holes in anti de Sitter five, is broadly similar, but with some differences. One of these is that, because the spatial rotation group, O4, is of rank 2, there are two rotation parameters, a & b. Each of these must have absolute value less than l to the minus one, for the co-rotation velocity to be less than the speed of light, all the way out to infinity. If just one of a & b, approaches the limiting value, the action of the black hole, and the partition function of the conformal field theory, both diverge in a manner similar to the four dimensional case.
Action of five-dimensional Kerr-AdS
But if a = b, and they approach the limit together, the action and the partition function, both have the same stronger divergence. Again, I haven't compared residues, but this might be worth doing. It may be that in the critical angular velocity limit, the interactions between the particles of super Yang Mills theory, become unimportant. If this is the case, one would expect the action and partition function to agree, rather than differ by a factor of four thirds, as in the non rotating case.
Asymptotically locally flat
I now turn the case of Nut charge. For asymptotically locally flat metrics in four dimensions, the reference background is the self-dual Taub Nut solution. The Taub bolt solution, has the same asymptotic behavior, but with the zero-dimensional nut fixed point, replaced by a two-dimensional bolt. The area of the bolt is 12 pi N squared, where N is the Nut charge. The area of the Misner string is minus 6 pi N squared. That is to say, the area of the Misner string in Taub bolt, is infinite, but it is less than the area of the Misner string in Taub nut, in a well-defined sense. The Hamiltonian on the Misner string, is N over 8. Again the Misner string Hamiltonian is infinite, but the difference from Taub nut, is finite. And the period, beta, is 8pi N. Thus the entropy, is pi N squared. Note that this is less than a quarter the area of the bolt, which would give 3 pi N squared. It is the effect of the Misner string that reduces the entropy.
Taub Nut Anti de Sitter
We would like to confirm the effect of Misner strings on entropy, by seeing what effect they have on conformal field theories, on the boundary of anti de Sitter space. For this purpose we constructed versions of Taub nut and Taub bolt, with a negative cosmological constant. The Taub nut anti de Sitter metric is shown on the transparancy. The parameter E, is the squashing of the three-sphere at infinity. If E=1, the three spheres are round, and the metric is Euclidean anti de Sitter space. However, if E is not equal to one, the metric can not be matched to anti de Sitter space at large distance. Each value of E, therefore, defines a different sector of ALADS metrics. This is an important point, which did not seem to have been realized by Chamblin et al. Taub Bolt Anti de Sitter One can also find a family of Taub bolt anti de Sitter metrics, with the same asymptotic behavior. These are characterized by an integer, k, and a positive quantity, s. These determine the asymptotic squashing parameter, E, and the area of the bolt, A-. K is the self-intersection number of the bolt. Thus the spaces do not have spin structure if k is odd. At infinity, the squashed three sphere has k points identified around the U1 fiber. This means that the reference background, is Taub nut anti de Sitter, with k points identified. If k is greater than one, the reference background will have an orbifold singularity at the nut. However, as I said earlier, I shall take it that such singularities are harmless.
Action
To calculate the action, one matches the Taub bolt solution on a squashed three sphere, to a Taub nut solution. To do this, one has to re-scale the squashing parameter, E, as a function of radius. The surface term in the action, is the same asymptotically for Taub nut and Taub bolt. Thus the action comes entirely from the difference in volumes.
Action for k = 1
For k greater than one, the action is always negative, while for k=1, it is positive for small areas of the bolt, and negative for large areas. This behavior is similar to that for Schwarzschild anti de Sitter space, and might indicate a phase transition in the corresponding conformal field theory. However, as I will argue later, there are problems with the ADS, CFT duality, if k=1. On the other hand, our results seem to indicate that there will be no phase transition, if more than one point is identified around the fiber. It will be interesting to see if this is indeed the case, for a conformal field theory on an identified squashed three-sphere.
In these Taub bolt anti de Sitter metrics, one can calculate the area of the Misner string, and the Hamiltonian surface term. Both will be infinite, but if one matches to Taub nut anti de Sitter on a large squashed three-sphere, the differences will tend to finite limits. As in the asymptotically locally flat case, the entropy is less than a quarter the area of the bolt, because of the effect of the Misner string.
Entropy
One can also calculate the entropy from the partition function, by the usual thermodynamic relations. The mass will be given by taking the derivative of the action with respect to beta. This is equal to the Hamiltonian surface term at infinity. The mass or energy, is the only charge that is constrained in the ensemble. The nut charge is fixed by the boundary conditions, and so doesn't need a La-grange multiplier. Thus the entropy is beta M, minus I. This agrees with the entropy calculated from the bolts and Misner strings, showing our definition, is consistent.
Formally at least, one can regard Euclidean conformal field theory on the squashed three sphere, as a twisted 2+1 theory, at a temperature, beta to the minus one. Thus one would expect the entropy to be proportional to beta to the minus two, at least for small beta. This has been confirmed by calculations by Dowker, of the determinants of scalar and fermion operators on the squashed three sphere, for k=1.
Dowker has not so far calculated the higher k cases, but one would expect that these would have similar leading terms, but with beta replaced by beta over k. The next leading order terms in the determinant, are beta to the minus one, log beta. No terms like this appear in the bulk theory, so if there really is an ADS, CFT duality in this situation, the log beta terms have to cancel between the different spins.
In fact, the scalar and fermion log beta terms will cancel each other, if there are twice as many scalars as fermions. This would be implied by super symmetry, suggesting that super symmetry is indeed necessary for the ADS, CFT duality.
The Misner string contributions to the entropy are of order beta squared. Thus Dowker's calculations will have to be extended to this order, to k greater than one, to fermion fields with anti periodic boundary conditions, and to spin one fields. All this is quite possible, but it will probably require Dowker to do it.
One might ask, how can a conformal field theory on the Euclidean squashed three sphere, correspond to a theory in a spacetime of Lorentzian signature. The answer is that, unlike the Schwarzschild anti de Sitter case, one has to continue the period, beta, to imaginary values. This makes the spacetime periodic in real time, rather than imaginary time. One gets a 2+1 rotating spacetime, rather like the Goedel universe, with closed time like curves. Although field theory in such a spacetime, may seem pathological, it can be obtained by analytical continuation, and is well defined despite the lack of causality. It is interesting that the analytically continued entropy, is negative, suggesting that causality violating spacetimes, are quantum suppressed. However, it is probably a mistake, to attach physical significance, to the Lorentzian conformal field theory.
To sum up, I discussed the ADS, CFT duality in two new contexts. That of rotating black holes and that of solutions with nut charge. I showed how gravitational entropy can be defined in general. The partition function for a thermodynamic ensemble can be defined by a path integral over periodic metrics. The lowest order contributions to the partition function will come from metrics with a U1 isometry, and given behavior at infinity. The entropy of such metrics will receive contributions from horizons or bolts, and from Misner strings, which are the Dirac strings of the U1 isometry, under Kaluza Klein reduction. One would like to relate this gravitational entropy, to the entropy of a conformal field theory on the boundary. For this reason, we considered a new class of asymptotically locally anti de Sitter spaces. Other people have investigated the Maldacena conjecture, by deforming the compact part of the metric, but this is the first time deformed anti de Sitter boundary conditions, have been considered.
We studied Taub bolt anti de Sitter solutions, with Taub nut anti de Sitter, as the reference background. The entropy we obtained obeyed the right thermodynamic relations, and had the right temperature dependence, to be the entropy of a conformal field theory, on the squashed three sphere. Because the Taub bolt solutions for odd k, do not have spin structures, this may indicate that the anti de Sitter, conformal field theory correspondence, does not depend on super symmetry.
I will end by saying that gravitational entropy, is alive and well, 34 years on. But there's more to entropy, than just horizon area. We need to look at the nuts and bolts.
TheCigSmokingMan
Rift Surfer
Re: Royal Airforce contact me about John
Darby,
I am naturally a suspicious person... /ttiforum/images/graemlins/smile.gif
However, words on these boards can have many contexts...
I understand your perspective of the word "ENTERTAINMENT"...
What I don't know for sure is the word "GAME" really means /ttiforum/images/graemlins/smile.gif or WHO it really INVOLVES... /ttiforum/images/graemlins/smile.gif
Probably, what the many different scenarios I described earlier for EricCarr and Titorite...
I would think its too obvious... You can't sell a 'script' that promotes CIVIL WAR based on currents and reality... /ttiforum/images/graemlins/smile.gif
Your information that you researched is most likely a cover operation /ttiforum/images/graemlins/smile.gif
I have throughly enjoyed THE GAME and hopefully made it my own /ttiforum/images/graemlins/smile.gif
TheCigMan
Darby,
I am naturally a suspicious person... /ttiforum/images/graemlins/smile.gif
However, words on these boards can have many contexts...
I understand your perspective of the word "ENTERTAINMENT"...
What I don't know for sure is the word "GAME" really means /ttiforum/images/graemlins/smile.gif or WHO it really INVOLVES... /ttiforum/images/graemlins/smile.gif
Probably, what the many different scenarios I described earlier for EricCarr and Titorite...
I would think its too obvious... You can't sell a 'script' that promotes CIVIL WAR based on currents and reality... /ttiforum/images/graemlins/smile.gif
Your information that you researched is most likely a cover operation /ttiforum/images/graemlins/smile.gif
I have throughly enjoyed THE GAME and hopefully made it my own /ttiforum/images/graemlins/smile.gif
TheCigMan