What does the existence of CTC imply for the Causal Structure of the spacetime? Can a strongly causal spacetime have any CTC[without fluctuating the metric]? Is there any such example? Can someone share please? I'd really appreciate if so.
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The existence of CTC creates problems in the predictivity of the theory. It prevents the foliation of space-time.
In general, if one has CTC confined to a region, this region will have compactly generated Cauchy horizons, on which Wald et al. have shown that it is not possible to renormalize the stress-energy tensor of a QFT, leading to an infinite burst in energy.
A strongly causal spacetime do not contains CTCs.
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1$\begingroup$ Could you please give a proof or reference where it is shown that strongly causal spacetime doesn't have CTC? Thanks $\endgroup$ Aug 4 at 17:10
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2$\begingroup$ "Spacetimes in which the events from the future can influence their past i.e. spacetimes in which there are closed causal curves do not satisfy Strong causality. From this point of view strong causality seems like a sensible physical requirement." from rohankulkarni.me/project/causal_structure/causal_structure.pdf $\endgroup$– PipeAug 4 at 17:12
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$\begingroup$ And by strongly casual you do not mean Stably strongly causal, you mean only and only strongly causal. Right? I know that CTC cannot exist in the case of Stably strongly causal only. @Pipe $\endgroup$ Aug 4 at 18:02
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$\begingroup$ @BastamTajik Stably strongly causal means that even if we perturb the metric we do not break the strong causal condition. So, yes in the answer I meant only strongly causal. $\endgroup$– PipeAug 4 at 18:35