Dilatonic black holes in gravity’s rainbow with a nonlinear source: the effects of thermal fluctuations

Abstract

This paper is devoted to an investigation of nonlinearly charged dilatonic black holes in the context of gravity's rainbow with two cases: (1) by considering the usual entropy, (2) in the presence of first order logarithmic correction of the entropy. First, exact black hole solutions of dilatonic Born-Infeld gravity with an energy dependent Liouville-type potential are obtained. Then, thermodynamic properties of the mentioned cases are studied, separately. It will be shown that although mass, entropy and the heat capacity are modified due to the presence of a first order correction, the temperature remains independent of it. Furthermore, it will be shown that divergences of the heat capacity, hence phase transition points are also independent of a first order correction, whereas the stability conditions are highly sensitive to variation of the correction parameter. Except for the effects of a first order correction, we will also present a limit on the values of the dilatonic parameter and show that it is possible to recognize AdS and dS thermodynamical behaviors for two specific branches of the dilatonic parameter. In addition, the effects of nonlinear electromagnetic field and energy functions on the thermodynamical behavior of the solutions will be highlighted and dependency of critical behavior, on these generalizations will be investigated. a

Dilaton black holes with power law electrodynamics

“…The conserved electric charge of the black holes can be obtained by calculating the total electric flux measured by an observer located at infinity with respect to the horizon (i.e. r → ∞ ) [50,56]. It can be obtained with the help of Gauss's electric law which can be written as [43,57]…”

Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?

“…The PM NED theory is richer than linear Maxwell's theory and in a special case (unit power), reduces to linear Maxwell's theory [33][34][35][36][37][38]. In is notable that the coupling of PM NED theory with gravity always is an interesting subject which attracted significant attentions because of specific properties [39][40][41][42][43][44][45][46][47][48][49][50]. Another attractive feature of the PM NED theory is related to its conformal invariant.…”

Energy dependent topological Black holes in Massive gravity coupled to Double-Logarithmic Electrodynamics

“…Rotating black branes in Gauss-Bonnet gravity and the corresponding thermodynamical properties are also studied in the presence of NLED [130]. Furthermore, the dilatonic black holes are also investigated in [131,132]. Besides inclusions of dark energy in the framework, non-linear electromagnetic fields are also introduced for the study of inflation period in early age of universe [133,134].…”