Stability of AdS in Einstein Gauss Bonnet Gravity

TL;DR

This paper investigates how adding a Gauss-Bonnet term to Einstein gravity affects the stability of Anti-de Sitter spacetime, showing that it can prevent black hole formation for small perturbations and thus restore stability.

Contribution

It demonstrates that Einstein-Gauss-Bonnet gravity in five dimensions stabilizes AdS spacetime against small perturbations, contrasting with pure Einstein gravity.

Findings

Presence of a radius gap in Choptuik scaling

Finite mass function as horizon radius approaches zero

Numerical simulations reveal complex horizon formation structure

Abstract

Recently it has been argued that in Einstein gravity Anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass/energy content of the spacetime is too small, thereby restoring the stability of AdS spacetime in this context. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.