Strength of the null singularity inside black holes

TL;DR

This paper analytically investigates the null singularity at the Cauchy horizon inside charged black holes, demonstrating its weak nature and the termination of all causal geodesics at this singularity, even with non-linear effects.

Contribution

It provides an analytical study of the null singularity inside charged black holes coupled with a scalar field, emphasizing its weak and deformationally-weak characteristics.

Findings

All causal geodesics terminate at the null singularity.

The singularity is weak according to Tipler's classification.

The singularity remains weak even at late retarded times with non-linear effects.

Abstract

We study analytically the Cauchy horizon singularity inside spherically-symmetric charged black holes, coupled to a spherical self-gravitating, minimally-coupled, massless scalar field. We show that all causal geodesics terminate at the Cauchy horizon at a null singularity, which is weak according to the Tipler classification. The singularity is also deformationally-weak in the sense of Ori. Our results are valid at arbitrary points along the null singularity, in particular at late retarded times, when non-linear effects are crucial.