https://doi.org/10.1140/epjc/s10052-016-3943-x
Regular Article - Theoretical Physics
A class of black holes in dRGT massive gravity and their thermodynamical properties
1
Centre of Theoretical Physics, Jamia Millia Islamia, New Delhi, 110025, India
2
Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of Kwazulu-Natal, Private Bag 54001, Durban, 4000, South Africa
3
Department of Physics, Faculty of Science, Mahidol University, Bangkok, 10400, Thailand
4
The Institute for Fundamental Study, Naresuan University, Phitsanulok, 65000, Thailand
5
Thailand Center of Excellence in Physics, Ministry of Education, Bangkok, 10400, Thailand
* e-mail: sgghosh@gmail.com
Received:
20
November
2015
Accepted:
10
February
2016
Published online:
4
March
2016
We present an exact spherical black hole solution in de Rham, Gabadadze, and Tolley (dRGT) massive gravity for a generic choice of the parameters in the theory, and also discuss the thermodynamical and phase structure of the black hole in both the grand canonical and the canonical ensembles (for the charged case). It turns out that the dRGT black hole solution includes other known solutions to the Einstein field equations, such as the monopole-de Sitter–Schwarzschild solution with the coefficients of the third and fourth terms in the potential and the graviton mass in massive gravity naturally generates the cosmological constant and the global monopole term. Furthermore, we compute the mass, temperature and entropy of the dRGT black hole, and also perform thermodynamical stability analysis. It turns out that the presence of the graviton mass completely changes the black hole thermodynamics, and it can provide the Hawking–Page phase transition which also occurs for the charged black holes. Interestingly, the entropy of a black hole is barely affected and still obeys the standard area law. In particular, our results, in the limit 
, reduced exactly to the results of general relativity.
© The Author(s), 2016
