Strong Cosmic Censorship in accelerating spacetime

TL;DR

This paper investigates the stability of the Cauchy horizon in accelerating black holes within Einstein-scalar theory, revealing violations of the Strong Cosmic Censorship Conjecture in near-extremal and flat limits without charge or rotation.

Contribution

It provides the first example of a black hole violating SCCC in an almost flat, uncharged, non-rotating accelerating black hole setting.

Findings

SCCC is violated in near-extremal and flat limits for accelerating black holes.

Violations occur without charge or rotation, unlike previous cases.

Decay rates of scalar perturbations are linked to quasinormal modes.

Abstract

It has been established that Strong Cosmic Censorship Conjecture (SCCC) is respected by an asymptotically flat black hole with charge, but violated by a charged asymptotically de Sitter black hole. We studied the instability of the Cauchy horizon for an accelerating black hole in Einstein theory conformally coupled with a scalar field. The black hole is uncharged while having inner, outer, and acceleration horizons. In the limit of vanishing acceleration, denoted by $A \to 0$, it becomes asymptotically flat and extremal, with its acceleration horizon vanishing as well. By exploring the perturbation of the massless scalar field upon the accelerating black hole, whose decay rate is governed by the quasinormal mode spectra, we show that the SCCC is violated in the near-extremal regime and also in the $A\to 0^+$ limit. Our result is the first observation of a black hole violating the SCCC in an almost asymptotically Minkowskian flat regime, as well as the first example of a black hole violating the SCCC with neither charge nor rotation.