Gravitational Waves around a Naked Singularity -- Odd-Parity Perturbation of Lemaitre-Tolman-Bondi Space-Time --

TL;DR

This paper investigates the stability of naked singularities formed in dust cloud collapse by analyzing odd-parity gravitational perturbations, finding that these singularities are marginally stable against such linear perturbations.

Contribution

It provides the first analysis of the stability of naked singularities in Lemaitre-Tolman-Bondi space-time against odd-parity gravitational wave perturbations.

Findings

Perturbations remain well-behaved near the naked singularity.

Naked singularity formation is marginally stable against odd-parity modes.

Supports the potential physical relevance of naked singularities.

Abstract

The motion of a spherical dust cloud is described by the Lemaitre-Tolman-Bondi solution and is completely specified by initial values of distributions of the rest mass density and specific energy of the dust fluid. From generic initial conditions of this spherically symmetric collapse, there appears a naked singularity at the symmetric center in the course of the gravitational collapse of the dust cloud. So this might be a counter example to the cosmic censorship hypothesis. To investigate the genericity of this example, we examine the stability of the `nakedness' of this singularity against odd-parity modes of non-spherical linear perturbations for the metric, i.e., linear gravitational waves. We find that the perturbations do not diverge but are well-behaved even in the neighborhood of the central naked singularity. This means that the naked singularity formation process is marginally stable against the odd-parity modes of linear gravitational waves.