Beyond the veil: Inner horizon instability and holography

TL;DR

This paper demonstrates that scalar perturbations cause an instability at the inner horizon of rotating BTZ black holes, supporting strong cosmic censorship, and reveals a holographic signature of this instability in the dual CFT entanglement structure.

Contribution

It shows how wavepacket analysis reveals inner horizon instability in rotating BTZ black holes and connects this to holographic entanglement in the dual CFT.

Findings

Inner horizon instability confirmed by wavepacket analysis.

Holographic dual captures horizon instability via CFT entanglement.

Divergent stress-energy signals instability behind the event horizon.

Abstract

We show that scalar perturbations of the eternal, rotating 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 wavepackets avoid this difficulty, and are dominated at late times by quasinormal behavior. The wavepackets 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 wavepackets nevertheless have a divergent stress-energy at the inner horizon, signaling an instability. This instability, which is localized behind the event horizon, is detected holographically as a breakdown in the semiclassical computation of dual CFT expectation values in which the analytic behavior of wavepackets 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.