Universal regularization prescription for Lovelock AdS gravity

TL;DR

This paper introduces a universal boundary term prescription for Lovelock AdS gravity that ensures finite conserved quantities and Euclidean action, applicable across various dimensions and theories, including Einstein-Hilbert and Einstein-Gauss-Bonnet gravity.

Contribution

It provides a universal polynomial boundary term (Kounterterms series) that guarantees finiteness and well-posed variational principle for Lovelock AdS gravity in any dimension.

Findings

A background-independent conserved charge formula for asymptotic symmetries.

A generalized vacuum energy formula in odd dimensions.

Direct derivation of black hole entropy from Euclidean action regularization.

Abstract

A definite form for the boundary term that produces the finiteness of both the conserved quantities and Euclidean action for any Lovelock gravity with AdS asymptotics is presented. This prescription merely tells even from odd bulk dimensions, regardless the particular theory considered, what is valid even for Einstein-Hilbert and Einstein-Gauss-Bonnet AdS gravity. The boundary term is a given polynomial of the boundary extrinsic and intrinsic curvatures (also referred to as Kounterterms series). Only the coupling constant of the boundary term changes accordingly, such that it always preserves a well-posed variational principle for boundary conditions suitable for asymptotically AdS spaces. The background-independent conserved charges associated to asymptotic symmetries are found. In odd bulk dimensions, this regularization produces a generalized formula for the vacuum energy in Lovelock AdS gravity. The standard entropy for asymptotically AdS black holes is recovered directly from the regularization of the Euclidean action, and not only from the first law of thermodynamics associated to the conserved quantities.