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.
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.