Lifshitz-like black holes in three and four dimensional F(R) gravity's rainbow

Abstract

Taking into account a special class of F(R) gravity, we obtain new Lifshitz-like black hole solutions in three and four dimensions in the context of gravity's rainbow. We discuss the geometric and thermodynamic properties of these solutions in the extended phase space and examine the first law of thermodynamics. Besides, we calculate the heat capacity to study thermal stability and possible phase transition. We find that the Lifshitz-like black holes in three dimensional spacetime are thermally stable while four dimensional black hole solutions undergo a van der Waals like phase transition.