Thermodynamic consequences of well-known regular black holes under modified first law

Abdul Jawad,Amna Khawer

doi:10.1140/epjc/s10052-018-6305-z

Abdul Jawad, Amna Khawer

Open Access

https://doi.org/10.1140/epjc/s10052-018-6305-z

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Abstract

We modify the first law of thermodynamics of regular black hole of the non-minimal Einstein–Yang–Mill theory with gauge field of magnetic Wu–Yang type and a regular black hole which is associated with the cosmological constant by the surface tensions. The corresponding Smarr relations are also satisfied for them. We calculate the Gibbs free energy to discuss the global stability of the black holes. It is found that Gibbs free energy exhibits the positive behavior in most of the cases which leads to globally thermodynamically stability of both black holes.

Highlights

In modern theoretical physics, black hole (BH) is an interesting subject
Cosmological constant will be associated with the pressure as P = − 8π and get modified laws for nonminimal magnetically charged regular black hole (MCRBH) in the stretched out phase space
The radial Einstein’s equation at the BH event horizon and cosmological horizon has been used in this paper in which we have obtained the modified first laws of thermodynamics for two BHs: (1) The non-minimal MCRBH and (2) regular black hole (RBH) with cosmological constant, for which all the correlated Smarr relations are satisfied

Summary

Introduction

Black hole (BH) is an interesting subject. At all times, BH is associated with a singularity inside it. Thermodynamical properties of the space-times proved to be very important and grasped the worthwhile attentions [23] They investigated the properties for the magnetically charged regular black hole (MCRBH). For the dS and AdS space-times, Chen, Qingyu and Tao, modified the first law of thermodynamics by the surface tension at the BH horizon and cosmological horizon [54]. Cosmological constant will be associated with the pressure as P = − 8π and get modified laws for nonminimal MCRBH in the stretched out phase space. 3, we modify the first law of thermodynamics at the BH horizon treating the cosmological constant as fixed by the surface tension and as associated with the pressure

Modification of First Law of Thermodynamics for non-minimal RBH

Fixed Cosmological Constant

Modifying Laws for RBH with Cosmological Constant

Conclusion