Conserved Charges for Even Dimensional Asymptotically AdS Gravity Theories

TL;DR

This paper develops a method to define finite, properly normalized conserved charges in even-dimensional asymptotically AdS gravity theories, avoiding background subtraction and ensuring consistency with local AdS boundary conditions.

Contribution

It introduces a boundary term in the action that guarantees finite conserved charges for solutions with locally AdS asymptotics in 2n dimensions, generalizing previous approaches.

Findings

Conserved charges are finite and correctly normalized without background subtraction.

Noether charges vanish for constant curvature spacetimes.

The zero cosmological constant case is recovered as a limit of AdS.

Abstract

Mass and other conserved Noether charges are discussed for solutions of gravity theories with locally Anti-de Sitter asymptotics in 2n dimensions. The action is supplemented with a boundary term whose purpose is to guarantee that it reaches an extremum on the classical solutions, provided the spacetime is locally AdS at the boundary. It is also shown that if spacetime is locally AdS at spatial infinity, the conserved charges are finite and properly normalized without requiring subtraction of a reference background. In this approach, Noether charges associated to Lorentz and diffeomorphism invariance vanish identically for constant curvature spacetimes. The case of zero cosmological constant is obtained as a limit of AdS, where $\Lambda $ plays the role of a regulator.