Conserved charges of black holes in Weyl and Einstein-Gauss-Bonnet gravities

TL;DR

This paper develops a new off-shell Noether current formulation to calculate conserved charges of various black holes in Weyl and Einstein-Gauss-Bonnet gravities, confirming previous results with a generalized approach.

Contribution

It introduces a novel off-shell Noether current based on the variation of the Bianchi identity, enabling the calculation of conserved charges in complex gravity theories.

Findings

Derived conserved charges for charged and dyonic black holes in Weyl and Einstein-Gauss-Bonnet gravities.

Validated the generalized formulation by matching results with existing methods.

Extended the applicability of off-shell Noether currents to diverse black hole solutions.

Abstract

An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge was recently proposed by Kim et al. They achieved this by introducing off-shell Noether currents and potentials. In this paper, we construct the crucial off-shell Noether current by the variation of the Bianchi identity for the expression of motion equation, with the help of the property of Killing vector. Our Noether current, which contains an additional term that is just one half of the Lie derivative of a surface term with respect to the Killing vector, takes a different form in comparison with the one in their work. Then we employ the generalized formulation to calculate the quasi-local conserved charges for the most general charged spherically symmetric and the dyonic rotating black holes with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the charged spherically symmetric black holes in arbitrary dimensional Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics in AdS spacetime. Our results confirm those through other methods in the literature.