Vacuum energy in Einstein-Gauss-Bonnet AdS gravity

TL;DR

This paper develops a finite action principle for Einstein-Gauss-Bonnet AdS gravity, providing a covariant vacuum energy formula and analyzing black hole thermodynamics in various dimensions.

Contribution

It introduces a boundary term functional for the action that differs in even and odd dimensions, ensuring well-posedness and correct thermodynamic descriptions.

Findings

Boundary term as maximal Chern form in even dimensions

Vacuum energy formula for odd-dimensional AdS spacetimes

Euclidean action reproduces black hole thermodynamics

Abstract

A finite action principle for Einstein-Gauss-Bonnet AdS gravity is presented. The boundary term, which is different for even and odd dimensions, is a functional of the boundary metric, intrinsic curvature and extrinsic curvature. For even dimensions, the boundary term corresponds to the maximal Chern form of the spacetime, and the asymptotic AdS condition for the curvature suffices for the well-posedness of this action. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. The background-independent Noether charges associated to asymptotic symmetries are found and the Euclidean continuation of the action correctly describes the black hole thermodynamics in the canonical ensemble. In particular, this procedure leads to a covariant formula for the vacuum energy in odd-dimensional asymptotically AdS spacetimes.