Abstract
We analyze the effects of thermal fluctuations on a regular black hole (RBH) of the non-minimal Einstein–Yang–Mill theory with gauge field of magnetic Wu–Yang type and a cosmological constant. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations corresponding to non-minimal RBH thermodynamics. In this scenario, we develop various important thermodynamical quantities, such as entropy, pressure, specific heats, Gibb’s free energy and Helmholtz free energy. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal RBH. We also discuss the stability of this RBH using various frameworks such as the gamma factor (the ratio of heat capacities), phase transition, grand canonical ensemble and canonical ensemble. It is observed that the non-minimal RBH becomes globally and locally more stable if we increase the value of the cosmological constant.
Highlights
The black hole (BH) solution is one of the most interesting phenomena in general relativity
Entropy and temperature, we have discussed the effect of thermal fluctuation on non-minimal regular black hole (RBH)
We observed that the pressure reduces due to the logarithmic correction when decreasing the value of the cosmological constant
Summary
The black hole (BH) solution is one of the most interesting phenomena in general relativity. Ashtekar has obtained such logarithmic corrections for BTZ BHs by calculating the exact partition function [8] These terms could be generated by the effects of string theory on the entropy of the BH. New regular exact spherically symmetric solutions of a non-minimal Einstein–Yang–Mills theory with a gauge field of magnetic Wu–Yang and cosmological constant are presented by Balakin et al [28,29]. We will use logarithmic correction terms to discuss various thermodynamical quantities, such as pressure, entropy, specific heats, Gibb’s free energy and Helmholtz free energy of non-minimal RBH. 2, we discuss RBHs of the non-minimal Einstein–Yang–Mill theory with gauge field of magnetic Wu–Yang type and a cosmological constant; we will find logarithmic correction terms which produces various thermodynamical quantities.
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