Cosmic Censorship for Self-Similar Spherical Dust Collapse

Abstract

We undertake a rigorous study of the stability of the Cauchy horizon in the naked self-similar Lemaitre-Tolman-Bondi spacetimes under even parity linear perturbations. We use a combination of energy methods and results about L^p-spaces to determine the behaviour of the perturbations as they evolve through the spacetime. We first establish that an average of the perturbation generically diverges on the Cauchy horizon. We next introduce a rescaled version of the perturbation, and show that it is bounded and non-zero on the Cauchy horizon. This in turn shows that the perturbation itself diverges in a pointwise fashion on the Cauchy horizon. We give a physical interpretation of this result using the perturbed Weyl scalars. This result supports the hypothesis of cosmic censorship.

49 pages, 3 figures

References in corpus (1)

• Odd-parity perturbations of self-similar Vaidya spacetime

Cited by in corpus (5)

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• Conformal diagrams for the gravitational collapse of a spherical dust cloud
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• Energy emission from high curvature region and its backreation
• Cauchy horizon stability in a collapsing spherical dust cloud I: geometric optic approximation and spherically symmetric test fields