Thermodynamic instability of nonlinearly charged black holes in gravity’s rainbow

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

doi:10.1140/epjc/s10052-016-3994-z

Abstract

Motivated by the violation of Lorentz invariancy in quantum gravity, we study black hole solutions in gravity's rainbow in context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered with an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate thermal stability conditions for these black hole solutions in context of canonical ensemble. We show that thermodynamical structure of the solutions depends on the choices of nonlinearity parameters, charge and energy functions.

Highlights

In doubly special relativity, there are two fundamental constants; the velocity of light and the Planck energy
The doubly special relativity has been generalized to curved spacetime, and this doubly general theory of relativity is called gravity’s rainbow [15,16]
In gravity’s rainbow, the energy of the test particle affects the geometry of spacetime

Summary

Introduction

There are two fundamental constants; the velocity of light and the Planck energy. If a particle is described by the standard model, the upper limit of the Planck energy is enforced and energy functions will have to satisfy mentioned condition, whereas in trans-planckian physics such a condition could be violated It means that the particle probing spacetime could acquire energies larger than the Planck energy. As we consider black holes in gravity’s rainbow, the energy E corresponds to the energy of a quantum particle in the neighborhood of the event horizon, which is emitted in the Hawking radiation [24,31,32,33,34]. Where E is the energy of a particle near the horizon, which is bounded by the Planck energy EP and cannot increase to arbitrary values This bound on the energy modifies temperature and entropy of the black hole in gravity’s rainbow [24].

Field equations and metric function

Conserved and thermodynamic quantities

Thermodynamic stability

Closing remarks