The Black hole Black string phase transition in Einstein-Gauss-Bonnet gravity

TL;DR

This paper explores the phase transition between black holes and black strings in Einstein-Gauss-Bonnet gravity at large dimensions, analyzing how different parameters influence the merger point geometry and potential topology changes.

Contribution

It provides new insights into the black hole-black string transition in Einstein-Gauss-Bonnet gravity, especially regarding the effects of the Gauss-Bonnet parameter on the merger geometry.

Findings

Merger point geometry can differ depending on the Gauss-Bonnet parameter range.

In some cases, the geometry does not approach a black hole away from the neck.

Potential topology-changing phase transition remains plausible under certain conditions.

Abstract

We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol. However as the merger point geometry does not approach the black hole geometry asymptotically it is not obvious that the transition is directly to a black hole phase. We also demonstrate that for another range of the Gauss-Bonnet parameter, the merger point geometry approaches the black hole geometry asymptotically when a certain parameter depending on the Gauss-Bonnet parameter $\alpha$ and on the parameters in the Einstein-Gauss-Bonnet black hole metric is small enough.