Odd-parity perturbations of the self-similar LTB spacetime

Emily M Duffy (1) , Brien C Nolan (1)

1 School of Mathematical Sciences

We consider the behaviour of odd-parity perturbations of those selfsimilar Lematre-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.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Emily M Duffy, Brien C Nolan. Odd-parity perturbations of the self-similar LTB spacetime. Classical and Quantum Gravity, 2011, 28 (10), pp.105020. ⟨10.1088/0264-9381/28/10/105020⟩. ⟨hal-00699375⟩