Back-in-Time and Faster-than-Light Travel in General Relativity by Serguei Krasnikov

Author:Serguei Krasnikov
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Proof

Let be a future-directed horizon generator lying in at all . Since is past inextendible, the parameter l is unbounded from below, see Proposition 13. Hence, we can define an infinite sequence of points , . Denote by the velocities of in the points . Due to the compactness of both and the sphere (12), there is a subsequence such that

where is a null vector satisfying (12). Consider a maximal geodesic emanating from with the initial velocity . By Corollary 7, is closed, so is one of its generators.

Suppose, is not a sought-for curve. But by construction it is a null geodesic inextendible in both directions. So, the only possibility is that at some d, which by the closedness of implies, in particular, that around there exists a coordinate ball B disjoint with . This means that every geodesic emanating from a point sufficiently close to p with initial velocity sufficiently close to also meets B and thus leaves . In particular, this is true for the segment of bounded by and with sufficiently large i. A contradiction.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.