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Analytic Study of Odd Parity Perturbations of self-similar LTB spacetimes

We consider the behaviour of odd-parity perturbations of the self-similar Lemaitre-Tolman-Bondi spacetimes which admit a naked singularity. We use the gauge invariant Gerlach-Sengupta formalism to analytically study the evolution of initially finite perturbations as they approach the Cauchy horizon. It is found that such perturbations remain finite on the Cauchy horizon, where finiteness refers to Sobolev norms of relevant perturbation scalars on spacelike hypersurfaces which are natural to the spacetime, as well as pointwise values of these quantities. This result applies to both metric and matter gauge invariant perturbations. We briefly consider the even-parity case using the same formalism.

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