Gravitational Radiation from a Naked Singularity. II - Even-Parity Perturbation -

TL;DR

This paper investigates the behavior of even-parity gravitational waves near a naked singularity in a collapsing dust model, finding that perturbations grow and diverge at the Cauchy horizon, indicating potential instability.

Contribution

It provides a numerical analysis of even-parity gravitational wave perturbations in the Lemaître-Tolman-Bondi spacetime, revealing divergence at the Cauchy horizon.

Findings

Perturbations grow near the Cauchy horizon.

Divergence of metric perturbation indicates instability.

Naked singularity is not a strong source of gravitational radiation.

Abstract

A naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study the even-parity mode of gravitational waves from a naked singularity of the Lema\^{\i}tre-Tolman-Bondi spacetime. The wave equations for gravitational waves are solved by numerical integration using the single null coordinate. The result implies that the metric perturbation grows when it approaches the Cauchy horizon and diverges there, although the naked singularity is not a strong source of even-parity gravitational radiation. Therefore, the Cauchy horizon in this spacetime should be unstable with respect to linear even-parity perturbations.