Isolated horizons in higher-dimensional Einstein-Gauss-Bonnet gravity

TL;DR

This paper extends the isolated horizon framework to higher-dimensional Einstein-Gauss-Bonnet gravity, deriving a covariant phase space and a generalized entropy formula consistent with other methods.

Contribution

It introduces a covariant phase space for EGB gravity in arbitrary dimensions and derives a new horizon entropy formula incorporating Gauss-Bonnet corrections.

Findings

Derived the first law for EGB black holes.

Established the entropy formula involving Ricci scalar and Gauss-Bonnet term.

Confirmed agreement with Euclidean and Noether charge methods.

Abstract

The isolated horizon framework was introduced in order to provide a local description of black holes that are in equilibrium with their (possibly dynamic) environment. Over the past several years, the framework has been extended to include matter fields (dilaton, Yang-Mills etc) in D=4 dimensions and cosmological constant in $D\geq3$ dimensions. In this article we present a further extension of the framework that includes black holes in higher-dimensional Einstein-Gauss-Bonnet (EGB) gravity. In particular, we construct a covariant phase space for EGB gravity in arbitrary dimensions which allows us to derive the first law. We find that the entropy of a weakly isolated and non-rotating horizon is given by $\mathcal{S}=(1/4G_{D})\oint_{S^{D-2}}\bm{\tilde{\epsilon}}(1+2\alpha\mathcal{R})$. In this expression $S^{D-2}$ is the $(D-2)$-dimensional cross section of the horizon with area form $\bm{\tilde{\epsilon}}$ and Ricci scalar $\mathcal{R}$, $G_{D}$ is the $D$-dimensional Newton constant and $\alpha$ is the Gauss-Bonnet parameter. This expression for the horizon entropy is in agreement with those predicted by the Euclidean and Noether charge methods. Thus we extend the isolated horizon framework beyond Einstein gravity.