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

Abstract

In this paper, we work on the topological Lifshitzlike 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.

Charged black hole chemistry with massive gravitons

“…The roots of the metric function V (r) = g rr = 0 specify the number of horizons, and, as reported in Refs. [32,55,64], the metric function V (r) could have more than two roots. So the multi-horizon black hole solutions are found in massive gravity and we assume that r + is the event horizon radius of the black hole solutions, i.e., the largest real positive root of V (r) = 0.…”

“…where the specific volume v is proportional to r + as v = 4r + ℓ d2 P /d 2 [5,10,27,29,30,32]. So, because of the dependency between r + , v and the thermodynamic volume V , criticality in one of P − r + , P − v or P − V planes indicates criticality in the others.…”

“…We now discuss the reentrant behavior of phase transition (first seen in [6,10]) in the canonical ensemble. As stated in [32], the RPT phenomenon can appear when the equation of state could give birth to two critical points in which the associated pressures and temperatures are positive definite, but, it is seen that only one of these critical points, referred to as (T C , P C ), is physical and the other one is unphysical since it cannot minimize the Gibbs free energy. By further studying the phase space, it will be evident that a virtual triple point (T T r , P T r ) and another critical point (T Z , P Z ) emerge.…”

“…These critical behaviors have been observed in a vast range of black hole configurations including nontrivial electromagnetic fields [9][10][11] and higher order curvatures [12][13][14][15][16][17][18][19][20][21][22][23]. But the story is different in dRGT massive gravity theory [24,25] since all topological black holes (TBHs) can experience critical behavior and phase transition due to the massive graviton self-interaction potentials [26][27][28][29][30][31][32]. From the AdS/CFT perspective [34,35], it leads to new prospects for investigating critical behavior of TBHs since there exists a dual * email address: ali.dehghani.phys@gmail.com † email address: hendi@shirazu.ac.ir interpretation in the gauge field theory (CFT) living on the AdS boundary.…”

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

“…gravity. In view of this, various investigations have been discussed with respected to the thermodynamics in the f (R) spacetimes [48][49][50][51]. In these studies, they found that the laws of thermodynamics of f (R) black hole was true.…”