No time machines in classical general relativity

Abstract

Theorem. 1) Any spacetime U has a maximal extension M max such that all closed causal curves in M max (if they exist there) are confined to the chronological past of U.2) The assertion remains true, even if the definition of spacetime is complemented by an arbitrary local geometric condition C.Obviously the meaning and the validity of the second part of the theorem depends crucially on what is understood by "local" and "geometric". The latter term is transparent-a condition is called geometric, iff it holds in a spacetime M, when and only when it holds in any spacetime isometric to M-but the situation with locality is more subtle. In [1] the following inadequate definition crept into the text:1. Definition. We call a condition C local if the following is true: C holds in a spacetime M if and only if it holds in any U which is isometric to an open subset of M. 2. Definition. The condition (property) C is local, if for any open covering {V α } of an arbitrary spacetime M the following equivalence is true ‡The two definitions are not equivalent. For example, the former is satisfied by thenon-local according to definition 2-property "to have timelike diameter § not greater than 1". Definition 2 is closer to the intuitive notion of locality: in particular, it makes the implication ( * ) true, which solves all the problems mentioned above. Thus, the only correction needed by [1] is the replacement of definition 1 by definition 2. ‡ Cf. "particularly interesting conditions" imposed on properties in Appendix B of [4].§ See [5] for definition.

Time Travel and Time Machines

“…It seems that if hole freeness is not required of the admissible extensions, then there always exists a smooth, maximal extension with CTCs that can be gained by the scissorsand-glue method. 54 Trivially, those spacetimes which already are maximal and thus admit of no non-trivial extension beyond the Cauchy horizon will not be extendible in a way that includes a non-vanishing region V. Thus, the conjecture has to be reformulated as claiming that for all spacetimes that permit a non-trivial extension beyond their Cauchy horizon, there exists a suitable smooth, maximal extension containing CTCs. Furthermore, once one adds the constraint of hole freeness, as we did above, it seems as if the scissors-and-glue method is no longer possible in general.…”

Chronological Spacetimes without Lightlike Lines are Stably Causal

“…In principle this fact does not mean that a chronology violating region can not develop from regular data. For this to be the case stronger global assumptions than the only absence of lightlike lines should be assumed [29,13].…”

“…The idea that such a mechanism should indeed exist and that starting from well behaved initial conditions closed timelike curves can not form has been referred by Hawking as the chronology protection conjecture [10]. As I commented above there is no general consensus on its validity and the evidence coming from classical general relativity is under investigation [29,28,32,13].…”

No no-go: A remark on time machines

“…We simply claim that Krasnikov's (2002) time machine no-go result, as presented, cannot be true. In addition, we prove a positive statement: a time machine existence theorem under a modest "no holes" assumption.…”

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AbstractWe present a counterexample to Krasnikov's (2002) much discussed time machine no-go result. In addition, we prove a positive statement: a time machine existence theorem under a modest "no holes" assumption.

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