Asymptotically Lifshitz black hole solutions in F(R) gravity

TL;DR

This paper derives asymptotically Lifshitz black hole solutions within F(R) gravity, analyzing their geometry, stability, and similarities to Einstein-Lambda-power-Maxwell black holes, without involving matter fields.

Contribution

It presents new Lifshitz black hole solutions in F(R) gravity and explores their geometric properties and stability criteria, expanding understanding of pure gravity solutions.

Findings

Solutions exhibit an essential singularity at the origin.

Solutions are analogous to Einstein-Lambda-power-Maxwell black holes.

Stability analysis via Dolgov-Kawasaki criterion confirms their viability.

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.