Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity

TL;DR

This work develops a Hamilton-Jacobi-based holographic renormalization scheme for Einstein-Gauss-Bonnet gravity to linear order in the Gauss-Bonnet coupling $\alpha$. By deriving covariant boundary counterterms that cancel power-law divergences, the authors compute the renormalized on-shell action and boundary stress tensor for asymptotically AdS Gauss-Bonnet black holes, including charged configurations. They obtain explicit expressions for the renormalized thermodynamic potential $\Omega$, energy $E$, temperature $T$, and entropy $S$ (via the Wald formula), and verify agreement with traditional background-subtraction results. The study also clarifies the significance of finite counterterms and discusses extensions to higher-derivative corrections and other curvature invariants, reinforcing the consistency of holographic thermodynamics with higher-curvature gravity.

Abstract

The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton-Jacobi method to calculate the boundary counterterms necessary to remove the divergences and allow the study of the thermodynamics of Einstein-Gauss-Bonnet black holes.