Covariant Symplectic Structure and Conserved Charges of New Massive Gravity

TL;DR

This paper develops a covariant symplectic framework for gravity theories, enabling the derivation of conserved charges, including for New Massive Gravity, and demonstrates its consistency with known results.

Contribution

It introduces a covariant symplectic structure applicable to various gravity theories, providing a unified way to compute conserved charges, including for New Massive Gravity.

Findings

Covariant symplectic current is conserved for any diffeomorphism-invariant gravity theory.

A closed Poincare invariant 2-form on phase space is constructed.

Conserved charges for NMG solutions are computed and agree with previous results.

Abstract

We show that the symplectic current obtained from the boundary term, which arises in the first variation of a local diffeomorphism invariant action, is covariantly conserved for any gravity theory described by that action. Therefore, a Poincare invariant 2-form can be constructed on the phase space, which is shown to be closed without reference to a specific theory. Finally, we show that one can obtain a charge expression for gravity theories in various dimensions, which plays the role of the Abbott-Deser-Tekin (ADT) charge for spacetimes with non-constant curvature backgrounds, by using the diffeomorphism invariance of the symplectic 2-form. As an example, we calculate the conserved charges of some solutions of New Massive Gravity (NMG) and compare the results with the previous works.