Quasi-Spherical Gravitational Collapse in Any Dimension

TL;DR

This paper investigates the formation of naked singularities in higher-dimensional Szekeres dust models with a cosmological constant, revealing that initial density profiles influence singularity visibility in dimensions above five.

Contribution

It extends the analysis of gravitational collapse and naked singularities to non-spherical, higher-dimensional space-times without symmetries, highlighting the role of initial density in such scenarios.

Findings

Naked singularities can occur in higher dimensions depending on initial data.

The nature of initial density influences the visibility of singularities.

Results are similar to those in spherically symmetric Tolman-Bondi-Lemaître models.

Abstract

We study the occurrence and nature of naked singularities for a dust model with non-zero cosmological constant in ($n+2$)-dimensional Szekeres space-times (which possess no Killing vectors) for $n\geq 2$. We find that central shell-focusing singularities may be locally naked in higher dimensions but depend sensitively on the choice of initial data. In fact, the nature of the initial density determines the possibility of naked singularity in space-times with more than five dimensions. The results are similar to the collapse in spherically symmetric Tolman-Bondi-Lema\^{\i}tre space-times.