A note on spherically symmetric naked singularities in general dimension

TL;DR

This paper extends a theorem on the non-existence of certain naked singularities in spherical collapse to higher dimensions and different topologies, analyzing various matter models and their implications for theoretical physics scenarios.

Contribution

It generalizes a recent theorem to higher dimensions and alternative topologies, and examines the applicability to common matter models and AdS scenarios.

Findings

Extension to higher dimensions and topologies is straightforward.

More general matter content restricts the class of excluded naked singularities.

Common matter theories satisfy the theorem's assumptions.

Abstract

We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider extending the theorem (1) to higher dimensions, (2) by including more general matter represented by a stress-energy tensor satisfying certain assumptions, and (3) by replacing the spherical geometry by a toroidal or higher genus (locally hyperbolic) one. We show that the extension to higher dimensions and a more general topology is straightforward; on the other hand, replacing the scalar field by a more general matter content forces us to shrink the class of naked singularities we are able to exclude. We then show that the most common matter theories (scalar field interacting with a non-abelian gauge field and a perfect fluid satisfying certain conditions) obey the assumptions of our weaker theorem, and we end by commenting on the applicability of our results to the five-dimensional AdS scenarii considered recently in the literature.