Spherically symmetric solutions and gravitational collapse in brane-worlds

TL;DR

This paper explores spherically symmetric solutions and gravitational collapse in brane-world models, deriving interior solutions, analyzing their properties, and examining the effects of bulk influences on star mass and collapse dynamics.

Contribution

It introduces new interior solutions for brane-world stars without junction conditions, and analyzes gravitational collapse with static exteriors in this framework.

Findings

Bulk effects have minimal impact on interior solutions.

Upper mass limit for static brane-world stars is established.

Exterior of collapsing star can remain static in brane-world scenarios.

Abstract

We consider spherically symmetric solutions within the context of brane-world theory without mirror symmetry or any form of junction conditions. For a constant curvature bulk, we obtain the modified Tolman-Oppenheimer-Volkoff (TOV) interior solutions in two cases where one is matched to a schwarzschild-de Sitter exterior while the other is consistent with an exterior solution whose structure can be used to explain the galaxy rotation curves without postulating dark matter. We also find the upper bound to the mass of a static brane-world star and show that the influence of the bulk effects on the interior solutions is small. Finally, we investigate the gravitational collapse on the brane and show that the exterior of a collapsing star can be static in this scenario.