Phase transition of charged Black Holes in Brans–Dicke theory through geometrical thermodynamics

Abstract

In this paper, we take into account black hole solutions of Brans-Dicke-Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and compare its results with those, calculated in the canonical ensemble through heat capacity. We show that these black holes enjoy second order phase transitions. We also show that there is a lower bound for the horizon radius of physical charged black holes in Brans-Dicke theory, which originates from restrictions of positivity of temperature. In addition, we find that employing a specific thermodynamical metric in the context of geometrical thermodynamics yields divergencies for the thermodynamical Ricci scalar in places of the phase transitions. It will be pointed out that due to the characteristic behavior of the thermodynamical Ricci scalar around its divergence points, one is able to distinguish the physical limitation point from the phase transitions. In addition, the free energy of these black holes will be obtained and its behavior will be investigated. It will be shown that the behavior of the free energy in the place where the heat capacity diverges demonstrates second order phase transition characteristics.

Thermodynamic stability of the stationary Lifshitz black hole of new massive gravity

“…The second one is considered by Mirza and Mansoori (MM) in [32][33][34][35], which is based on conjugate thermodynamic potentials, specifically chosen to reflect the relevant thermodynamic properties of system under consideration. Some applications of these approaches to different gravitational systems can be found for example in [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. In order to identify the admissible thermodynamic metrics for a given black hole solution, a case by case study is required.…”

Heat engines for dilatonic Born–Infeld black holes

“…BD (Brans-Dicke) theory has been significant in the explanation of the cosmic inflation [46], and consistent with Dirac's large number hypothesis and Mach's principle [47,48]. Thermodynamics of charged black holes in Brans-Dicke theory have been studied in [49][50][51][52]. This theory produces the solar system experimental observations with a specific domain of BD parameter ω [53].…”

Charged BTZ black holes in the context of massive gravity’s rainbow

“…Recent studies in the context of the GTs approaches for the black hole thermodynamics have shown that the Ricci scalars of Weinhold, Ruppeiner and Quevedo metrics may lead to extra divergencies which are not matched with the bound points and the phase transitions [97][98][99][100]. In other words, there were cases of mismatch between divergencies of the Ricci scalar and the mentioned points (bound and phase transition points), and also existence of extra divergency unrelated to these points were reported [97][98][99][100]. In order to overcome the shortcomings of the mentioned methods (Weinhold, Ruppeiner and Quevedo metrics), the HPEM method was introduced and it was shown that the specific structure of this metric provides satisfactory results regarding GTs of different classes of the black holes.…”

“…[97][98][99][100], for more details). In other words, obtained results of these three approaches were not consistent with those extracted from other methods.…”