Gravitational collapse and singularity avoidance of a homogeneous dust fluid on a brane with timelike extra dimension

TL;DR

This paper studies how a homogeneous dust cloud collapsing in a braneworld model with an extra timelike dimension avoids forming a singularity, due to finite brane tension and bounded scalar curvature.

Contribution

It demonstrates that in a specific braneworld model, gravitational collapse does not lead to singularities because of the effects of the extra timelike dimension and finite brane tension.

Findings

Scalar curvature remains finite during collapse

Collapse results in a static Reissner Nordstrom exterior

Brane effects prevent singularity formation

Abstract

We investigate the gravitational collapse of a homogeneous dust cloud in the Shtanov Sahni braneworld model, which incorporates an extra timelike dimension. The interior of the collapsing configuration is modeled by a Friedmann Lemaitre spacetime, while the exterior is described by a Vaidya radiation envelope that eventually settles into a static Reissner Nordstrom (RN) geometry with a positive tidal charge. Although a smooth matching between the interior and the static exterior is precluded by the breakdown of Birkhoff's theorem in the braneworld scenario, we show that as long as braneworld effects remain significant, the brane tension stays finite. Consequently, the scalar curvature remains bounded, thereby preventing the formation of a singularity.