Conserved charges for gravity with locally AdS asymptotics

TL;DR

This paper introduces a new formula for conserved charges in 3+1 gravity with local AdS asymptotics, defining mass and angular momentum without background subtraction, applicable even as the cosmological constant approaches zero.

Contribution

It proposes a boundary term based on the Euler density that yields conserved charges directly from the action for spacetimes with local AdS asymptotics.

Findings

Mass and angular momentum are obtained as Noether charges without background subtraction.

Negative constant curvature spacetimes have vanishing conserved charges.

The approach remains valid as the cosmological constant tends to zero.

Abstract

A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the limit of vanishing cosmological constant.