Spherical trapped surfaces in n-dimensional general relativity

TL;DR

This paper investigates gravitational collapse in n-dimensional general relativity, analyzing how initial matter profiles influence trapped surfaces and singularity formation, with results indicating generic horizon coverage of singularities.

Contribution

It provides a detailed analysis of trapped surfaces in higher-dimensional collapse models considering various matter types and initial conditions, clarifying the role of initial data in singularity formation.

Findings

Trapped regions depend on initial velocity and density profiles.

Central singularities are generally covered by horizons under broad conditions.

The study extends understanding of gravitational collapse in higher dimensions.

Abstract

In this paper, we examine gravitational collapse of matter fields in $n$-dimensional general relativity. The matter energy-momentum tensor under consideration includes dust, perfect fluids with equations of state and matter admitting bulk and shear viscosity. By adjusting various parameters of the matter energy-momentum tensor, we determine the trapped region and spherical marginally trapped surfaces in homogeneous and inhomogeneous models of collapse. We show that, as expected, the time development of marginally trapped tube is intricately related to the initial velocity and density profiles of the collapsing matter configuration. This study clarifies the role of initial data in the formation of spacetime singularity during gravitational collapse and implies that, under generic conditions on the matter profiles, the central spacetime singularity is always covered by a horizon.