Higher dimensional charged $f(R)$ black holes

TL;DR

This paper introduces a new class of higher-dimensional charged black hole solutions in $f(R)$ gravity coupled with conformally invariant Maxwell fields, revealing unique properties and phase transitions in specific dimensions.

Contribution

It constructs higher-dimensional charged black holes in $f(R)$ gravity with conformally invariant Maxwell fields, analyzing their thermodynamics and stability, which was not previously explored.

Findings

Black hole solutions exist only in dimensions that are multiples of four.

The solutions obey the first law of thermodynamics and have a Smarr-type relation.

A phase transition is identified in the stability analysis.

Abstract

We construct a new class of higher dimensional black hole solutions of $f(R)$ theory coupled to a nonlinear Maxwell field. In deriving these solutions the traceless property of the energy-momentum tensor of the matter filed plays a crucial role. In $n$-dimensional spacetime the energy-momentum tensor of conformally invariant Maxwell field is traceless provided we take $n=4p$, where $p$ is the power of conformally invariant Maxwell lagrangian. These black hole solutions are similar to higher dimensional Reissner-Nordstrom AdS black holes but only exist for dimensions which are multiples of four. We calculate the conserved and thermodynamic quantities of these black holes and check the validity of the first law of black hole thermodynamics by computing a Smarr-type formula for the total mass of the solutions. Finally, we study the local stability of the solutions and find that there is indeed a phase transition for higher dimensional $f(R)$ black holes with conformally invariant Maxwell source.