Extended phase space of AdS black holes in Einstein–Gauss–Bonnet gravity with a quadratic nonlinear electrodynamics

Abstract

In this paper, we consider quadratic Maxwell invariant as a correction to the Maxwell theory and study thermodynamic behavior of the black holes in Einstein and Gauss-Bonnet gravities. We consider cosmological constant as a thermodynamic pressure to extend phase space. Next, we obtain critical values in case of variation of nonlinearity and Gauss-Bonnet parameters. Although the general thermodynamical behavior of the black hole solutions is the same as usual Van der Waals system, we show that in special case of the nonlinear electromagnetic field, there will be a turning point for the phase diagrams and usual Van der Waals is not observed. This theory of nonlinear electromagnetic field provides two critical horizon radii. We show that this unusual behavior of phase diagrams is due to existence of second critical horizon radius. It will be pointed out that the power of the gravity and nonlinearity of the matter field modify the critical values. We generalize the study by considering the effects of dimensionality on critical values and make comparisons between our models with their special sub classes. In addition, we examine the possibility of the existence of the reentrant phase transitions through two different methods.

Charged dilatonic black holes in gravity’s rainbow

“…There are several reasons for such a consideration; e.g. one can point out the existence of a second order phase transition for black holes, Van der Waals like liquid/gas behavior in phase diagrams, and the formation of the triple point [91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108][109]. The consideration of the cosmological constant as a thermodynamical variable could be supported by studies that are conducted in the context of AdS/CFT [120][121][122][123].…”

“…In addition, it was shown that a case of ensemble dependency exists for charged three-dimensional black holes which could be removed by considering the cosmological constant as a thermodynamical variable [124]. The thermodynamical critical behavior of black holes in the presence of different matter fields and gravities has been investigated in the literature [91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108][109].…”

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

“…One of the most important property of this method is the similarity of critical behavior of the black holes and ordinary thermodynamical Van der Waals liquid/gas systems [75][76][77][78][79][80][81][82][83][84][85][86][87]. Recently, it was pointed out that the extended phase space should be interpreted as an RG-flow in the space of field theories, where isotherm curves codify how the number of degrees of freedom N (or the central charge c) runs with the energy scale [88].…”

“…Using the renewed interpretation of the cosmological constant as thermodynamical pressure, one can use following relation to rewrite thermodynamical relations of the solutions in spherical horizon [75][76][77][78][79][80][81][82][83][84][85][86][87] …”

Interaction between two point-like charges in nonlinear electrostatics

“…[6][7][8][9][10][11][12] and the references therein) with finite selfa e-mail: breev@mail.tsu.ru b e-mail: shabad@lpi.ru energy of the point charge, allied to their famous prototype, the Born-Infeld model [13], where the finiteness of the field is achieved at the cost of square-root nonanalyticity of the Lagrangian, which leads to an infinity to the Maxwell equation. The most popular application [6][7][8][9][10][11][12][14][15][16][17][18][19][20][21][22]] of these models is to combine them with General Relativity in order to study their effect on the initial singularity and on the evolution of the Universe. In contrast to the Born-Infeld model, the models from the class of Ref.…”