Asymptotically Lifshitz black hole solutions in F(R) gravity

Abstract

We consider a class of spherically symmetric spacetime to obtain some interesting solutions in F(R) gravity without matter field (pure gravity). We investigate the geometry of the solutions and find that there is an essential singularity at the origin. In addition, we show that there is an analogy between obtained solutions with the black holes of Einstein-Lambda -power-Maxwell-invariant theory. Furthermore, we find that these solutions are equivalent to the asymptotically Lifshitz black holes. Also, we calculate d^2F/dR^2 to examine the Dolgov-Kawasaki stability criterion.