Structure of the Cauchy horizon singularity

TL;DR

This paper investigates the nature of the Cauchy horizon singularity in a charged black hole perturbed by a scalar field, revealing it to be weak and analytically characterizable at different sections.

Contribution

It provides the first detailed numerical and analytical analysis of the weak singularity structure at the Cauchy horizon of a charged black hole with scalar perturbations.

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 and verified.

Metric perturbations vanish in the early section, consistent with perturbation theory.

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 perturbations vanish, 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.