Stability of naked singularities and algebraically special modes

TL;DR

This paper demonstrates that algebraically special modes cause instability in certain naked singularity spacetimes with negative mass, with stability depending on boundary conditions, and discusses extensions to charged and rotating cases.

Contribution

It reveals the instability of negative-mass naked singularities due to algebraically special modes and explores boundary condition effects on stability.

Findings

Negative-mass Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable.

Stability of Schwarzschild-anti-de Sitter depends on boundary conditions.

Results extend to charged and rotating singularities.

Abstract

We show that algebraically special modes lead to the instability of naked singularity spacetimes with negative mass. Four-dimensional negative-mass Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable. Stability of the Schwarzschild-anti-de Sitter spacetime depends on boundary conditions. We briefly discuss the generalization of these results to charged and rotating singularities.