Are the singularities stable?

TL;DR

This paper investigates the stability of spacetime singularities within Einstein-Maxwell models with scalar fields, demonstrating stability against axial perturbations through analysis of perturbation equations.

Contribution

It provides a detailed stability analysis of static spherically symmetric solutions with scalar fields, specifically proving axial stability in this context.

Findings

Stability against axial perturbations established.

Perturbation equations derived for the model.

Singularities shown to be stable under certain conditions.

Abstract

The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we have analyzed the general problem of stability of the family of the static spherically symmetric solutions of the standard Einstein-Maxwell model coupled to an extra free massless scalar field. We have obtained the equations for the axial and polar perturbations. The stability against axial perturbations has been proven.