Alternative approach to the regularization of odd dimensional AdS gravity

TL;DR

This paper introduces a new boundary term in odd-dimensional AdS gravity that ensures finite actions and charges, based on a symmetry principle, and demonstrates its effectiveness with Schwarzschild-AdS black holes.

Contribution

The paper proposes an alternative boundary term for odd-dimensional AdS gravity derived from a symmetry principle, providing a new regularization method for finite actions and charges.

Findings

Finite Euclidean action for Schwarzschild-AdS black holes.

Finite conserved charges, including mass, for black holes.

The boundary term yields correct thermodynamics.

Abstract

In this paper I present an action principle for odd dimensional AdS gravity which consists of introducing another manifold with the same boundary and a very specific boundary term. This new action allows and alternative approach to the regularization of the theory, yielding a finite euclidean action and finite conserved charges. The choice of the boundary term is justified on the grounds that an enhanced 'almost off-shell' local AdS/Conformal symmetry arises for that very special choice. One may say that the boundary term is dictated by a guiding symmetry principle. Two sets of boundary conditions are considered, which yield regularization procedures analogous to (but different from) the standard 'background substraction' and 'counterterms' regularization methods. The Noether charges are constructed in general. As an application it is shown that for Schwarszchild-AdS black holes the charge associated to the time-like Killing vector is finite and is indeed the mass. The Euclidean action for Schwarzschild-AdS black holes is computed, and it turns out to be finite, and to yield the right thermodynamics. The previous paragraph may be interpreted in the sense that the boundary term dictated by the symmetry principle is the one that correctly regularizes the action.