https://doi.org/10.1140/epjc/s10052-016-4550-6
Regular Article - Theoretical Physics
Revisiting conserved charges in higher curvature gravitational theories
1
Michigan Center for Theoretical Physics, Randall Laboratory of Physics, University of Michigan, Ann Arbor, MI, 48109-1040, USA
2
School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
3
Department of Science, Campus of Bijar, University of Kurdistan, Bijar, Iran
* e-mail: kamalhajian@ipm.ir
Received:
10
November
2016
Accepted:
1
December
2016
Published online:
20
December
2016
Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called the “solution phase space method,” conserved charges are unambiguous and regular. Moreover, assuming the generators of the charges to be exact symmetries, entropies and other conserved charges can be calculated on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be a local identity relating the exact symmetries to which the mass, angular momentum, electric charge, and entropy are attributed. In this paper, we apply this powerful method to the f(R) gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include warped AdS
, charged static BTZ, and 3-dimensional 
Lifshitz black holes.
© The Author(s), 2016
