Vacuum Energy in Odd-Dimensional AdS Gravity

TL;DR

This paper introduces a background-independent method for calculating conserved charges in odd-dimensional AdS gravity, providing a consistent action principle and matching known vacuum energy results for topological black holes.

Contribution

It presents a novel Lorentz-covariant approach with boundary conditions on extrinsic and Lorentz curvature, avoiding background dependence and standard counterterms.

Findings

Provides a well-defined action principle in any odd dimension.

Regularizes Euclidean action and reproduces black hole thermodynamics.

Vacuum energy matches conjectured expressions for all odd dimensions.

Abstract

A background-independent, Lorentz-covariant approach to compute conserved charges in odd-dimensional AdS gravity, alternative to the standard counterterms method, is presented. A set of boundary conditions on the asymptotic extrinsic and Lorentz curvature, rather than a Dirichlet boundary condition on the metric is used. With a given prescription of the boundary term, a well-defined action principle in any odd dimension is obtained. The same boundary term regularizes the Euclidean action and gives the correct black hole thermodynamics. The conserved charges are obtained from the asymptotic symmetries through Noether theorem without reference to any background. For topological AdS black holes the vacuum energy matches the expression conjectured by Emparan, Johnson and Myers \cite{Emparan-Johnson-Myers} for all odd dimensions.