Odd Parity Perturbations of the Self-Similar LTB Spacetime

Details Odd Parity Perturbations of the Self-Similar LTB Spacetime Odd Parity Perturbations of the Self-Similar LTB Spacetime

2010-12-13

arxiv.org/abs/1012.2766v2

Class. Quantum Grav. 28: 105020, 2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

36 pages

Scientific paper

We consider the behaviour of odd-parity perturbations of those self-similar Lema\^{i}tre-Tolman-Bondi spacetimes which admit a naked singularity. We find that a perturbation which evolves from initially regular data remains finite on the Cauchy horizon. Finiteness is demonstrated by considering the behaviour of suitable energy norms of the perturbation (and pointwise values of these quantities) on natural spacelike hypersurfaces. This result holds for a general choice of initial data and initial data surface. Finally, we examine the perturbed Weyl scalars in order to provide a physical interpretation of our results. Taken on its own, this result does not support cosmic censorship; however a full perturbation of this spacetime would include even parity perturbations, so we cannot conclude that this spacetime is stable to all linear perturbations.

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