Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method

TL;DR

This paper develops a boundary counterterm method to compute the action and charges of asymptotically anti-de Sitter black objects in Einstein-Gauss-Bonnet gravity, covering dimensions up to 9 and including various black hole solutions.

Contribution

It introduces a general counterterm framework for Einstein-Gauss-Bonnet theory in dimensions up to 9, enabling calculation of actions and charges for diverse black objects.

Findings

Derived explicit boundary counterterms for dimensions up to 9.

Applied the method to static, rotating, and string black solutions.

Validated the approach for different black object configurations.

Abstract

We propose to compute the action and global charges of the asymptotically anti-de Sitter solutions in Einstein-Gauss-Bonnet theory by adding boundary counterterms to the gravitational action. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension $d\leq 9$. We apply this tehnique for several different types of black objects. Apart from static and rotating black holes, we consider also Einstein-Gauss-Bonnet black string solutions with negative cosmological constant.