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The AdS/CFT correspondence has kindled interest in anti-de Sitter and asymptotically AdS spacetimes which are non-globally hyperbolic. That means a Cauchy horizon forms in these spacetimes. Moreover, recent interest has been put in the stability at the classical level.

On the other hand the Cosmic Censorship Conjecture are two mathematical conjectures about the structure of spacetime.

In particular, the so-called Strong Cosmic Conjecture asserts heuristically that generically, general relativity is a deterministic theory, in the same sense that classical mechanics is a deterministic theory. In other words, the classical fate of all observers should be predictable from suitable initial data.

A lot of work has been done in relevant physical spacetimes which assumes that spacetime must be asymptotically flat and in the case of Cauchy horizons forming inside black holes. See this for an example.

My questions are:

  1. Using the AdS/CFT correspondence, does the horizon is reflected somehow in the dual CFT?

  2. Is the Cauchy horizon of anti-de Sitter spacetime stable?

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This is interesting, see some general references below. To answer your question first:

  1. Yes -- I am not aware of the exact dual picture, but as far as I understand one can use the holographic No Transmission principle due to Engelhardt and Horowitz (see https://arxiv.org/abs/1509.07509 and my GRF essay https://arxiv.org/abs/2304.01292) to see how the independence of two CFTs must imply that the inner Cauchy horizon is unstable, so as to ensure the independence of the bulk duals.
  2. This is the general question of SCC in AdS, and as far as I know this is a very controversial question. See my essay and references therein to see some recent works on it. The best I can say is that one expects it to be unstable, although there are violations that one should also expect. I personally advocate the holographic (from NTP) and general semiclassical descriptions (which state that at nonlinear orders the inner Cauchy horizon is unstable even if not classically) rather than the brute-force computations that one does, but this is only up to a certain level.

[1] O. J. C. Dias, F. C. Eperon, H. S. Reall, and J. E. Santos, Phys. Rev. D 97, 104060 (2018), arXiv:1801.09694 [gr-qc].

[2] O. J. C. Dias, H. S. Reall, and J. E. Santos, JHEP 10, 001 (2018), arXiv:1808.02895 [gr-qc].

[3] R. Emparan and M. Tomaˇsevi´c, JHEP 06, 038 (2020), arXiv:2002.02083 [hep-th].

[4] N. Engelhardt and G. T. Horowitz, Phys. Rev. D 93, 026005 (2016), arXiv:1509.07509 [hep-th].

[5] O. J. C. Dias, H. S. Reall, and J. E. Santos, JHEP 12, 097 (2019), arXiv:1906.08265 [hep-th].

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