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

TL;DR

This paper presents analytical Lifshitz-like black hole solutions in a special class of three-dimensional F(R) gravity, analyzing their geometric, thermodynamic, and stability properties, and exploring phase transition possibilities.

Contribution

It introduces new Lifshitz-like black hole solutions in three-dimensional F(R) gravity and examines their thermodynamic behavior and stability, which was not previously studied.

Findings

Solutions behave like charged BTZ black holes in certain limits

Thermodynamic analysis confirms the first law and Smarr relation

Thermal stability and criticality potential are discussed

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.