A note on the Deser-Tekin charges

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.

LATEX, 7 pages, no figures

References in corpus (6)

• Relativistic conservation laws and integral constraints for large cosmological perturbations
• Conserved Charges of Higher D Kerr-AdS Spacetimes
• On the mass of a Kerr-anti-de Sitter spacetime in D dimensions
• On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations
• Conserved currents in $D$-dimensional gravity and brane cosmology
• Perturbations in the Einstein theory of gravity: Conserved currents

Cited by in corpus (12)

• Black hole mass and angular momentum in topologically massive gravity
• Universal regularization prescription for Lovelock AdS gravity
• Conserved Charges of Higher D Kerr-AdS Spacetimes
• Phase Transitions in Higher Derivative Gravity
• Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories
• Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities
• Three types of superpotentials for perturbations in the Einstein-Gauss-Bonnet gravity
• Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravity
• Field-theoretical construction of currents and superpotentials in Lovelock gravity
• On creating mass/matter by extra dimensions in the Einstein-Gauss-Bonnet gravity
• Conserved quantities for black hole solutions in pure Lovelock gravity
• Black holes of the Vaidya type with flat and (A)dS asymptotics as point particles