Quasi-local conserved charges and holography

TL;DR

This paper develops a quasi-local formalism for conserved charges in gravity theories with matter fields, establishing their equivalence with holographic and covariant phase space methods, applicable even with slow falloff behaviors at infinity.

Contribution

It introduces a new quasi-local formalism for conserved charges in gravity that is independent of Lagrangian ambiguities and proves their equivalence with holographic and phase space approaches.

Findings

The formalism yields conserved charges consistent with covariant phase space.

Boundary currents produce charges identical to those from the boundary stress tensor.

The approach extends existing equivalence results to more general matter field behaviors.

Abstract

We construct a quasi-local formalism for conserved charges in a theory of gravity in the presence of matter fields which may have slow falloff behaviors at the asymptotic infinity. This construction depends only on equations of motion and so it is irrespective of ambiguities in the total derivatives of the Lagrangian. By using identically conserved currents, we show that this formalism leads to the same expressions of conserved charges as those in the covariant phase space approach. At the boundary of the asymptotic AdS space, we also introduce an identically conserved boundary current which has the same structure as the bulk current and then show that this boundary current gives us the holographic conserved charges identical with those from the boundary stress tensor method. In our quasi-local formalism we present a general proof that conserved charges from the bulk potential are identical with those from the boundary current. Our results can be regarded as the extension of the existing results on the equivalence of conserved charges by the covariant phase space approach and by the boundary stress tensor method.