  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.

General Relativity and Quantum Cosmology