Near--extremal gravitational collapse in 4+1 dimensions: Schwarzschild--de--Sitter space

TL;DR

This paper numerically investigates near-extremal black hole formation in 4+1 dimensions from gravitational collapse, exploring implications for black hole thermodynamics in a cosmological setting.

Contribution

It provides the first numerical evidence of near-extremal horizon formation in higher-dimensional collapse within Einstein gravity with a positive cosmological constant.

Findings

Black holes with mass over 99% of extremal value form from collapse.

Results suggest the third law of black hole thermodynamics may not hold in cosmological contexts.

Evidence indicates extremality corresponds to the maximal mass of Schwarzschild-de Sitter black holes.

Abstract

We numerically study a formation of near extremal horizons from a gravitational collapse of radially symmetric gravitational waves in $4+1$ dimensions within the framework of pure Einstein gravity with positive cosmological constant. Evolution of a regular initial data with cosmological horizon leads to a formation of a black hole with mass exceeding $99\%$ of the extremal value corresponding to the black hole and cosmological horizons coinciding. We demonstrate how our results fit within the framework of characteristic gluing, and present some evidence that the third law of black hole thermodynamics may not hold in the cosmological context, where the extremality corresponds to the maximal mass of the Schwarzschild black hole in de--Sitter space.