Even perturbations of the self-similar Vaidya space-time
Nolan, Brien C.ORCID: 0000-0002-9356-6833 and Waters, Thomas J.
(2005)
Even perturbations of the self-similar Vaidya space-time.
Physical Review D, 71
(10).
pp. 104030-1.
ISSN 1550-7998
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.