Higher dimensional dust collapse with a cosmological constant

TL;DR

This paper derives exact solutions for higher-dimensional dust collapse with a cosmological constant, analyzing the formation of singularities and horizons, and finding that higher dimensions favor black hole formation over naked singularities.

Contribution

It provides the first exact interior solutions for higher-dimensional dust collapse with a cosmological constant and examines their causal structure and singularity formation.

Findings

Collapse proceeds similarly to Minkowski background with naked singularities.

Higher dimensions tend to favor black hole formation.

Solutions match exterior higher-dimensional Schwarzschild-de Sitter metrics.

Abstract

The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman-Bondi metrics imbedded in a de Sitter background. The solution is then matched to exterior HD Scwarschild-de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.