Thermal stability of a special class of black hole solutions in F(R) gravity

Abstract

In this paper, we work on the topological Lifshitz-like black hole solutions of a special class of vacuum $F(R)-$gravity that are static and spherically symmetric. We investigate geometric and thermodynamic properties of the solutions with due respect to the validity of the first law of thermodynamics. We examine the van der Waals like behavior for asymptotically AdS solutions with spherical horizon by studying the $P-v$, $G-T$ and $C_{Q,P}-r_{+}$ diagrams and find a consistent result. We also investigate the same behavior for hyperbolic horizon and interestingly find that the system under study can experience a phase transition with negative temperature.

14 pages with 7 captioned figures. Some additional notes are added. Accepted in EPJC

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Cited by in corpus (1)

• Violations of the weak cosmic censorship conjecture in the higher dimensional $f(R)$ black holes with pressure