Three dimensional Lifshitz-like black hole in a special class of F(R) gravity

S.H Hendi,R Ramezani-Arani,E Rahimi

doi:10.1016/j.physletb.2020.135436

S.H Hendi, R Ramezani-Arani + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2020.135436

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Abstract

Regarding a special class of pure F(R) gravity in three dimensions, we obtain, analytically, Lifshitz-like black hole solutions. We check the geometrical properties of the solutions which behave such as charged BTZ black holes in special limit. We also investigate the thermodynamic properties of the solutions and examine the first law of thermodynamics and Smarr formula. In addition, we study thermal stability via the heat capacity and discuss the possibility of criticality in the extended phase space.

Highlights

The generalization of Einstein’s Lagrangian to a more general invariant of the Riemann tensor, an arbitrary function of the Ricci scalar, is considered by Buchdahl in 1970 [1]
Considering the black hole as a thermodynamic system, one has to examine the validity of the first law and thermal stability
We have discussed geometrical properties of the solutions and found that these solutions reduce to charged BTZ like solutions in Einstein-Λ-PMI gravity

Summary

INTRODUCTION

The generalization of Einstein’s Lagrangian to a more general invariant of the Riemann tensor, an arbitrary function of the Ricci scalar, is considered by Buchdahl in 1970 [1]. The structure of this paper is as follows: At first, we obtain three dimensional Lifshitz-like black hole in the context of a special class of the F (R) gravity and investigate its geometric and thermodynamic properties. We find that the last term can be interpreted as a charge-term in power-Maxwell nonlinear electrodynamics with the following total charge In other words, such a metric function is completely in agreement with that of charged black hole solution of Einsteinpower Maxwell invariant (Einstein-PMI) gravity when the nonlinearity parameter is chosen s = dimension/4 which is conformally invariant Maxwell source. The general form of d−dimensional solutions is addressed in the appendix

THERMODYNAMIC BEHAVIOR AND THERMAL STABILITY

Conserved and thermodynamic quantities

Examine thermal stability and phase transition

Smarr relation

CONCLUSION