Abstract
We study the inner horizons of rotating and charged black holes in anti-de Sitter space. These black holes have a classical analytic extension through the inner horizon to additional asymptotic regions. If this extension survives in the quantum theory, it requires particular analytic properties in a dual CFT, which give a prescription for calculating correlation functions for operators placed on any asymptotic boundary of the maximally extended spacetime. We show that for charged black holes in three or greater dimensions, and rotating black holes in four or greater dimensions, these analytic properties are in- consistent in the dual CFT, implying the absence of an analytic extension for quantum fields past the inner horizon. Thus, we find that strong cosmic censorship holds for all AdS black holes except rotating BTZ. To further study the latter case, we insert classical perturbations near the boundary at late times, producing shockwaves traveling along the inner horizon. We holographically compute CFT correlators in this background that probe a high energy scattering process near the inner horizon and argue that the shockwave does not destabilize the inner horizon violently enough to prevent signaling between different asymptotic regions of the Penrose diagram. This provides evidence that the rotating BTZ black hole does violate the strong cosmic censorship conjecture.
Highlights
(figure 1).1 The maximal analytic extension of the spacetime continues infinitely in the past and future directions, and includes an infinite number of asymptotic regions
We present a proposal for analytic continuation of conformal field theory (CFT) correlators which places operators in different boundaries of the Penrose diagram for a rotating or charged thermal ensemble
In holography, the purified thermal charged ensemble is a state in a two-sided Hilbert space HCFT ⊗ HCFT, so by the usual mechanisms of anti-de Sitter (AdS)/CFT there should only be two asymptotic boundaries
Summary
Consider the boundary two point function of a neutral operator in a (possibly charged) black hole background, where the operators are spacelike separated, and carry an operator around the outer bifurcate horizon (left panel of figure 3). This gives rise to the periodicity condition. The Euclidean geometry does not explicitly represent the interior of the black hole, so it is more difficult to relate properties of the inner horizon to Euclidean boundary correlators This is why we find the above Lorentzian single valuedness condition convenient: it can be directly applied to the inner bifurcate horizon
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