Gravitational collapse in the AdS background and the black hole formation

TL;DR

This paper investigates the gravitational collapse of a massless scalar field in five-dimensional Anti-de Sitter space, analyzing horizon formation and black hole development through numerical solutions of Einstein's equations.

Contribution

It provides a detailed numerical analysis of scalar field collapse in AdS space, including the evolution of the Misner-Sharp mass and apparent horizon, highlighting the dynamics of black hole formation.

Findings

Misner-Sharp mass remains constant except across a thin shell.

Apparent horizon evolution indicates black hole formation.

Thermalization time depends on initial black hole horizon radius.

Abstract

We study the time evolution of the Misner-Sharp mass and the apparent horizon for gravitational collapse of a massless scalar field in the $AdS_{5}$ space-time for both cases of narrow and broad waves by numerically solving the Einstein's equations coupled to a massless scalar field. This is done by relying on the full dynamics of the collapse including the concept of the dynamical horizon. It turns out that the Misner-Sharp mass is everywhere constant except for a rapid change across a thin shell defined by the density profile of the collapsing wave. By studying the evolution of the apparent horizon, indicating the formation of a black hole at different times we see how asymptotically an event horizon forms. The dependence of the thermalization time on the radius of the initial black hole event horizon is also studied.