Odd-parity perturbations of self-similar Vaidya spacetime

TL;DR

This paper analytically investigates odd-parity perturbations of self-similar Vaidya spacetimes with naked singularities, demonstrating that such perturbations remain finite at the Cauchy horizon, indicating stability in this context.

Contribution

It provides the first detailed analysis showing that odd-parity perturbations stay finite at the Cauchy horizon in self-similar Vaidya spacetimes with naked singularities.

Findings

Perturbations remain finite at the Cauchy horizon

Finiteness holds for metric, matter, and Weyl curvature scalars

Results suggest stability of the spacetime under odd-parity perturbations

Abstract

We carry out an analytic study of odd-parity perturbations of the self-similar Vaidya space-times that admit a naked singularity. It is found that an initially finite perturbation remains finite at the Cauchy horizon. This holds not only for the gauge invariant metric and matter perturbation, but also for all the gauge invariant perturbed Weyl curvature scalars, including the gravitational radiation scalars. In each case, `finiteness' refers to Sobolev norms of scalar quantities on naturally occurring spacelike hypersurfaces, as well as pointwise values of these quantities.