Gravitational Radiation from a Naked Singularity: Odd-Parity Perturbation

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Abstract
It has been suggested that a naked singularity is a good candidate for a strong gravitational wave burster. A naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study the odd-parity mode of gravitational waves from a naked singularity of the Lemaître-Tolman-Bondi spacetime. The wave equation for gravitational waves is solved by numerical integration using the single null coordinate. It is found 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 spacetime should be marginally stable with respect to odd-parity perturbations.

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