Even perturbations of the self-similar Vaidya space-time
Nolan, Brien C. and Waters, Thomas (2005) Even perturbations of the self-similar Vaidya space-time. Physical Review D, 71 (10). 104030-1-104030-23. ISSN 1550-7998
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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 to impinge upon the Cauchy horizon (CH), where 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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