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

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.

Figures (1)

• Figure 1: $M_{\pm}$ are two partial Cauchy surfaces enclosing a region of space-time and intersecting $\Delta$ in the 3-surface $S_{\pm}$ respectively,and extend to spatial infinity $i^0$. Another Cauchy slice M is drawn which intersects $\Delta$ in $S_{\Delta}$