Beyond the veil: Inner horizon instability and holography

Abstract

We show that scalar perturbations of the eternal, rotating Banados-Teitelboim-Zanelli (BTZ) black hole should lead to an instability of the inner (Cauchy) horizon, preserving strong cosmic censorship. Because of backscattering from the geometry, plane-wave modes have a divergent stress tensor at the event horizon, but suitable wave packets avoid this difficulty, and are dominated at late times by quasinormal behavior. The wave packets have cuts in the complexified coordinate plane that are controlled by requirements of continuity, single-valuedness, and positive energy. Due to a focusing effect, regular wave packets nevertheless have a divergent stress energy at the inner horizon, signaling an instability. We propose that this instability, which is localized behind the event horizon, is detected holographically as a breakdown in the semiclassical computation of dual conformal field theory (CFT) expectation values in which the analytic behavior of wave packets in the complexified coordinate plane plays an integral role. In the dual field theory, this is interpreted as an encoding of physics behind the horizon in the entanglement between otherwise independent CFTs.