On the stability of naked singularities

TL;DR

This paper investigates the stability of the negative mass Schwarzschild solution with a naked singularity, identifying conditions under which it remains stable and highlighting a physically preferred boundary condition.

Contribution

It provides a precise stability criterion for naked singularities and identifies a physically preferred boundary condition ensuring stability.

Findings

The spacetime is stable under a specific boundary condition.

A one-parameter family of boundary conditions exists at the singularity.

Stability depends critically on the chosen boundary condition.

Abstract

We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise criterion for stability depending on the boundary condition. We show that one particular boundary condition is physically preferred and show that the spacetime is stable with this boundary condition.