Tolman-Bondi Space-Time in Brane World Scenario

TL;DR

This paper explores inhomogeneous Tolman-Bondi dust space-time models within brane world scenarios, presenting solutions that describe collapsing, expanding, and bouncing universes with potential black hole or naked singularity outcomes.

Contribution

It introduces two novel solutions for inhomogeneous dust models on the brane, including a collapsing/expanding model and a bouncing universe, expanding understanding of brane cosmology.

Findings

Collapse can lead to black holes or naked singularities.

Models exhibit transition from deceleration to acceleration.

Bouncing solutions occur at different radii and epochs.

Abstract

In the present work, inhomogeneous Tolman-Bondi type dust space-time is studied on the brane. There are two sets of solutions of the above model. The first solution represents either a collapsing model starting from an infinite volume at infinite past to the singularity or a model starting from a singularity and expanding for ever having a transition from decelerating phase to accelerating phase. The first solution shows that the end state of collapse may be black hole or a naked singularity depending signs of various parameters involved. The second solution represents a bouncing model where the bounce occurs at different comoving radii at different epochs.