Gravitational Radiation from a Naked Singularity -- Odd-Parity Perturbation --

TL;DR

This paper investigates whether naked singularities can produce strong odd-parity gravitational waves, finding that they are not significant sources despite metric perturbation growth, implying marginal stability of the Cauchy horizon.

Contribution

It provides a numerical analysis of odd-parity gravitational wave emission from naked singularities in Lemaître-Tolman-Bondi space-time, showing limited radiation output.

Findings

Naked singularities are not strong sources of odd-parity gravitational waves.

The metric perturbation grows centrally but does not lead to strong radiation.

The Cauchy horizon remains marginally stable against odd-parity perturbations.

Abstract

It has been suggested that a naked singularity may be a good candidate for a strong gravitational wave burster. The naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study odd-parity mode of gravitational waves from a naked singularity of the Lema\^{\i}tre-Tolman-Bondi space-time. The wave equation for gravitational waves are solved by numerical integration using the single null coordinate. The result is that the naked singularity is not a strong source of the odd-parity gravitational radiation although the metric perturbation grows in the central region. Therefore, the Cauchy horizon in this space-time would be marginally stable against odd-parity perturbations.