Einstein-Born-Infeld-massive gravity: adS-black hole solutions and their thermodynamical properties

Abstract

In this paper, we study massive gravity in the presence of Born-Infeld nonlinear electrodynamics. First, we obtain metric function related to this gravity and investigate the geometry of the solutions and find that there is an essential singularity at the origin (r = 0). It will be shown that due to contribution of the massive part, the number, type and place of horizons may be changed. Next, we calculate the conserved and thermodynamic quantities and check the validation of the first law of thermodynamics. We also investigate thermal stability of these black holes in context of canonical ensemble. It will be shown that number, type and place of phase transition points are functions of different parameters which lead to dependency of stability conditions to these parameters. Also, it will be shown how the behavior of temperature is modified due to extension of massive gravity and strong nonlinearity parameter. Next, critical behavior of the system in extended phase space by considering cosmological constant as pressure is investigated. A study regarding neutral Einstein-massive gravity in context of extended phase space is done. Geometrical approach is employed to study the thermodynamical behavior of the system in context of heat capacity and extended phase space. It will be shown that GTs, heat capacity and extended phase space have consistent results. Finally, critical behavior of the system is investigated through use of another method. It will be pointed out that the results of this method is in agreement with other methods and follow the concepts of ordinary thermodynamics.

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

“…[63][64][65][66]. Furthermore, it was shown that the mentioned massive gravity has sensible effects in metal/superconductor phase transition.…”

“…[62]. Moreover, the generalizations of such theory to include nonlinear electrodynamics, higher derivative gravity and gravity's rainbow have been done [63][64][65][66]. In addition, thermodynamic properties, phase transitions and thermal stability of such generalized models have…”

“…In other words, the pressure and horizon radius of the maximum are critical pressure and horizon radius. This method was employed in several paper [63,64,66,151]. Now, we employ this method to study critical behavior of the system.…”

Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity

“…In addition, the electromagnetic field tensor indimensions is given by tr = √ 2 3 /(1 + Γ)( / 2 ), and the metric function ( ) is obtained as follows [58]: ,…”

“…More discussions in various gravity theories can be found in . Recently, some investigations for thermodynamics of AdS black holes have been also generalized to the extended phase space in the dRGT massive gravity [47][48][49][50], which show the Van der Waals-like SBH/LBH phase transition in the charged topological AdS black holes. In addition, the deep relation between the dynamical perturbation and the Van der Waals-like SBH/LBH phase transition in the fourdimensional dRGT massive gravity has been also recovered in [51].…”