A note on the Deser-Tekin charges

TL;DR

This paper develops a generalized framework for conserved charges in arbitrary metric theories of gravity, extending Deser-Tekin currents to include matter fields and nonlinear effects, with applications to black hole mass calculations.

Contribution

It introduces a new family of conserved currents and superpotentials that generalize previous Deser-Tekin constructions for quadratic curvature gravity theories.

Findings

Constructed perturbed equations for arbitrary metric theories in D dimensions.

Derived a generalized family of conserved currents and superpotentials.

Applied the framework to compute the mass of a D-dimensional Schwarzschild black hole.

Abstract

Perturbed equations for an arbitrary metric theory of gravity in $D$ dimensions are constructed in the vacuum of this theory. The nonlinear part together with matter fields are a source for the linear part and are treated as a total energy-momentum tensor. A generalized family of conserved currents expressed through divergences of anti-symmetrical tensor densities (superpotentials) linear in perturbations is constructed. The new family generalizes the Deser and Tekin currents and superpotentials in quadratic curvature gravity theories generating Killing charges in dS and AdS vacua. As an example, the mass of the $D$-dimensional Schwarzschild black hole in an effective AdS spacetime (a solution in the Einstein-Gauss-Bonnet theory) is examined.