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

Physics of the Dark Universe, ISSN: 2212-6864, Vol: 33, Page: 100873
2021
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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.

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