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Even perturbations of self-similar Vaidya space-time

Brien C. Nolan·Thomas J. Waters
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Abstract

We study even parity metric and matter perturbations of all angular modes in self-similar Vaidya space-time. We focus on the case where the background contains a naked singularity. Initial conditions are imposed describing a finite perturbation emerging from the portion of flat space-time preceding the matter-filled region of space-time. The most general perturbation satisfying the initial conditions is allowed impinge upon the Cauchy horizon (CH), whereat the perturbation remains finite: there is no ``blue-sheet'' instability. However when the perturbation evolves through the CH and onto the second future similarity horizon of the naked singularity, divergence necessarily occurs: this surface is found to be unstable. The analysis is based on the study of individual modes following a Mellin transform of the perturbation. We present an argument that the full perturbation remains finite after resummation of the (possibly infinite number of) modes.

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Brien C. Nolan, Thomas J. Waters. 2005-05-09. Even perturbations of self-similar Vaidya space-time. https://doi.org/10.1103/physrevd.71.104030

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