Holographic Probes of Inner Horizons

TL;DR

This paper investigates the quantum properties of inner horizons in AdS black holes, showing most are unstable and violate strong cosmic censorship, except for rotating BTZ black holes which may allow signals across horizons.

Contribution

It demonstrates the inconsistency of analytic extensions past the inner horizon in dual CFTs for most AdS black holes, and provides evidence that rotating BTZ black holes violate strong cosmic censorship.

Findings

Inner horizons are generally unstable in quantum theory.

Strong cosmic censorship holds for all AdS black holes except rotating BTZ.

Shockwaves near the inner horizon do not prevent signaling, indicating potential violation of cosmic censorship in rotating BTZ.

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 inconsistent 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.