I registered several days ago, and I have the impression, that the people here are very competent in the theory of time travelling.Can you recommend me a real scientific book/ebook about this topic?
Try "Black Holes and Time Warps: Einstein's Outrageous Legacy" by Kip Thorne. Dr. Thorne is the former "Feynman Professor of Theoretical Physics" at Cal Tech. Professor John Wheeler was his PhD supervisor at Princeton. He's a bit beyond "very competent".