https://doi.org/10.1140/epjc/s10052-014-3156-0
Regular Article - Theoretical Physics
Conserved charges of black holes in Weyl and Einstein–Gauss–Bonnet gravities
1
Institute of Technical Physics, SEEE, Wuhan Textile University, Wuhan, Hubei, 430073, People’s Republic of China
2
Kavli Institute for Theoretical Physics China, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing, 100080, People’s Republic of China
* e-mail: pengjjph@163.com
Received:
17
August
2014
Accepted:
24
October
2014
Published online:
11
November
2014
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 EOM, 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 obtained through other methods in the literature.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
