Laws of black hole mechanics in the Einstein-Gauss-Bonnet theory

TL;DR

This paper extends the isolated horizon formalism to five-dimensional Einstein-Gauss-Bonnet gravity, deriving modified laws of black hole mechanics that incorporate corrections due to the Gauss-Bonnet term, including changes to horizon area and angular momentum.

Contribution

It introduces a formalism for rotating black holes in Einstein-Gauss-Bonnet theory and derives the modified laws of black hole mechanics with new boundary conditions.

Findings

Modified first law includes Gauss-Bonnet corrections

Provides boundary conditions for exact solutions

Shows Hamiltonian evolution on solution space

Abstract

We extend the isolated horizon formalism to include rotating black holes arising in five dimensional Einstein-Gauss-Bonnet (EGB) theory of gravity, and derive the laws of black hole mechanics. This result allows us to show that the first law of black hole mechanics is modified, due to the Gauss-Bonnet term, so as to include corrections to (i) the area of horizon cross-sections and, to (ii) the expression of horizon angular momentum. Once these modifications are included, the Hamiltonian generates an evolution on the space of solutions of the EGB theory admitting isolated horizon as an internal boundary, the consequence of which is the first law of black hole mechanics. These boundary conditions may help in the search for exact solutions describing rotating black holes in this theory.