Exact 2+1 dimensional rotating black hole solution in f (R)-gravity and its thermodynamical properties

In this work, we obtain the exact rotating black hole solution in f (R)-gravity model(R is not considered as a constant here) and investigate its thermodynamics, especially phase transition and critical behavior in the anti-de-Sitter (AdS) extended phase space. One particular characteristic of this solution is that when we set J = 0, the Massive BTZ black hole solution recovers. We also obtain the exact form of the f(R) model for this solution. In the thermodynamical analysis, we calculate the thermodynamical quantities like the temperature and entropy for this solution and we compare them with the BTZ corresponding quantities. Also, We show the validity of the first law of thermodynamics. After that, we investigate the stability(local and global) of this obtained solution. In the critical behavior analysis, we find that there is no evidence to show the existence of P -V criticality like the ordinary BTZ case. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The study focuses on obtaining the exact rotating black hole solution in the f(R)-gravity model and analyzing its thermodynamics, including comparison with the BTZ black hole solution. The validity of the first law of thermodynamics was demonstrated, and the stability of the obtained solution was investigated. No evidence of P-V criticality similar to the ordinary BTZ case was found.