Dilatonic black holes in gravity\u2019s rainbow with a nonlinear source: the effects of thermal fluctuations

S H Hendi,S Panahiyan,B Eslam Panah,M Momennia

doi:10.1140/epjc/s10052-017-5211-0

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.

Highlights

Albeit there extremely successful consequences of Einstein’s theory of gravity, there are various issues which signal that this theory should be modified, at least at high energy regime
It will be shown that divergences of the heat capacity, phase transition points are independent of a first order correction, whereas the stability conditions are highly sensitive to variation of the correction parameter
We have studied the black hole solutions in dilaton gravity’s rainbow in the presence of BI source

Summary

Introduction

Albeit there extremely successful consequences of Einstein’s theory of gravity, there are various issues which signal that this theory should be modified, at least at high energy regime. Following the gravity supplementing special relativity which leads to GR, one can generalize doubly special relativity in the presence of gravity to obtain the socalled doubly general relativity or gravity’s rainbow [18] Another way for constructing such theories is considering a modification of the standard energy-momentum relation. We have the following incomplete list showing the investigation of: gravitational fields coupled to BI NED for static black holes [94–101], wormholes [102,103], rotating black objects [104,105], and superconductors [106] Motivated by these applications, in this paper, we analyze dilaton field using the formalism of gravity’s rainbow in the presence of BI NED. In the present paper, we are going to study the dilatonic black hole solutions in Einstein gravity’s rainbow coupled to BI NED with considering the effects of thermal fluctuations

Black hole solutions of dilaton gravity’s rainbow in the presence of BI NED

Thermodynamics

Thermal fluctuations: correction

Thermal structure: comparison between correction and non-correction

Conclusion