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Gauge invariant perturbations of self-similar Lemaître-Tolman-Bondi spacetime: even parity modes with l≥2

Waters, Thomas and Nolan, Brien C. (2009) Gauge invariant perturbations of self-similar Lemaître-Tolman-Bondi spacetime: even parity modes with l≥2. Physical Review D, 79 (8). 084002-1-084002-13. ISSN 1550-7998

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Abstract

In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaître-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.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:general relativity; quantum cosmology;
Subjects:Mathematics
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Publisher:The American Physical Society
Official URL:http://dx.doi.org/10.1103/PhysRevD.79.084002
Copyright Information:© 2009 The American Physical Society
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
Funders:Enterprise Ireland
ID Code:15641
Deposited On:10 Aug 2010 10:13 by DORAS Administrator. Last Modified 10 Aug 2010 10:13

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