Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime

TL;DR

This paper constructs and analyzes inhomogeneous charged black hole solutions in anti-de Sitter space, showing the destruction of the Cauchy horizon and infinite tidal forces at the horizon, supporting cosmic censorship.

Contribution

It provides new analytical and numerical solutions for inhomogeneous charged black holes in AdS space and demonstrates the universal disappearance of the Cauchy horizon under perturbations.

Findings

Cauchy horizon always disappears under perturbations

Observers experience infinite tidal forces at the horizon

Supports the strong cosmic censorship conjecture

Abstract

We investigate static inhomogeneous charged planar black hole solutions of the Einstein-Maxwell system in an asymptotically anti-de Sitter spacetime. Within the framework of linear perturbations, the solutions are numerically and analytically constructed from the Reissner-Nordstr\"{o}m-AdS black hole solution. The perturbation analysis predicts that the Cauchy horizon always disappears for any wavelength perturbation, supporting the strong cosmic censorship conjecture. For extremal black holes, we analytically show that an observer freely falling into the black hole feels infinite tidal force at the horizon for any long wavelength perturbation, even though the Kretschmann scalar curvature invariant remains small.