Structure of the black hole's Cauchy horizon singularity

TL;DR

This paper investigates the structure of the Cauchy horizon singularity in a charged black hole perturbed by a scalar field, revealing its weak nature and providing analytical and numerical insights into its behavior.

Contribution

It demonstrates that the Cauchy horizon singularity is weak and provides exact analytical expressions for key field gradients, verified through numerical simulations.

Findings

The singularity is weak at both early and late sections of the CH.

Analytical expressions for gradients of r and scalar field are derived.

Numerical verification confirms the analytical results.

Abstract

We study the Cauchy horizon (CH) singularity of a spherical charged black hole perturbed nonlinearly by a self-gravitating massless scalar field. We show numerically that the singularity is weak both at the early and at the late sections of the CH, where the focusing of the area coordinate $r$ is strong. In the early section the metric is almost Reissner-Nordstr\"{o}m, and the fields behave according to perturbation analysis. We find exact analytical expressions for the gradients of $r$ and of the scalar field, which are valid at both sections. We then verify these analytical results numerically.