Scalar perturbations to naked singularities of perfect fluid

TL;DR

This paper investigates the instability of spherically symmetric naked singularities in Einstein-perfect fluid systems, demonstrating they are unstable under scalar field perturbations, which sheds light on their physical viability.

Contribution

It introduces a model showing that certain naked singularities are unstable to scalar perturbations, providing insights into their potential instability in more complex systems.

Findings

Naked singularities are unstable to scalar field perturbations.

Instability leads to trapped surface formation.

Results suggest naked singularities may not be physically stable.

Abstract

In this paper, we study the instability of naked singularities arising in the Einstein equations coupled with isothermal perfect fluid. We show that the spherically symmetric self-similar naked singularities of this system, are unstable to trapped surface formation, under $C^{1,\alpha}$ perturbations of an external massless scalar field. We viewed this as a toy model in studying the instability of these naked singularities under gravitational perturbations in the original Einstein--Euler system which is non-spherically symmetric.