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Gauge invariant perturbations of self-similar lemaître-tolman-bondi spacetime: even parity modes withl≥2

Waters, Thomas J.
Nolan, Brien C.
Identifiers
http://hdl.handle.net/10379/14396
https://doi.org/10.13025/26091
Repository DOI
Publication Date
2009-04-03
Type
Article
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Citation
Waters, Thomas J. Nolan, Brien C. (2009). Gauge invariant perturbations of self-similar lemaître-tolman-bondi spacetime: even parity modes withl≥2. Physical Review D 79 (8),
Abstract
In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaitre-Tolman-Bondi (timelike dust) spacetime containing a naked singularity. We decompose the angular part of the perturbation in terms of spherical harmonics and perform a Mellin transform to reduce the perturbation equations to a set of ordinary differential equations with singular points. We fix initial data so the perturbation is finite on the axis and the past null cone of the singularity, and follow the perturbation modes up to the Cauchy horizon. There we argue that certain scalars formed from the modes of the perturbation remain finite, indicating linear stability of the Cauchy horizon.
Funder
Publisher
American Physical Society (APS)
Publisher DOI
10.1103/physrevd.79.084002
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland