A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes II

TL;DR

This paper introduces a simplified mathematical model inspired by Einstein equations to study null singularity formation inside black holes, demonstrating finite-time blowup and features analogous to black-hole interior instabilities.

Contribution

It presents a new simplified hyperbolic semi-linear system modeling null singularities, providing insights into black-hole interior dynamics and singularity formation.

Findings

The system exhibits finite-time blowup.

The singularity formed is a null singularity.

Features resemble known black-hole interior instabilities.

Abstract

We study a simple system of two hyperbolic semi-linear equations, inspired by the Einstein equations. The system, which was introduced in gr-qc/0612136, is a model for singularity formation inside black holes. We show for a particular case of the equations that the system demonstrates a finite time blowup. The singularity that is formed is a null singularity. Then we show that in this particular case the singularity has features that are analogous to known features of models of black-hole interiors - which describe the inner-horizon instability. Our simple system may provide insight into the formation of null singularities inside spinning or charged black holes.