$(2+1)$-Dimensional Black Holes in $f(R,\phi)$ Gravity

TL;DR

This paper explores black hole solutions in a (2+1)-dimensional $f(R)$ gravity theory with a scalar field, revealing new solutions with potential thermodynamic advantages over known black holes.

Contribution

It introduces new black hole solutions in $f(R)$ gravity with scalar fields, showing how non-linear $f(R)$ terms affect black hole properties without fixing the $f(R)$ form.

Findings

Discovery of a massless black hole solution with non-linear Ricci scalar correction.

Recovery of known hairy black hole solutions when non-linear terms are absent.

Indication that the new black holes may have higher entropy, suggesting thermodynamic preference.

Abstract

We consider a $f(R)$ gravity theory in $(2+1)$-dimensions with a self-interacting scalar field non-minimally coupled to gravity. Without specifying the form of the $f(R)$ function, solving the field equations we find that the Ricci scalar receives a non-linear correction term which breaks the conformal invariance and leads to a massless black hole solution. When the non-linear term decouples, we get a well known hairy black hole solution with the scalar field conformally coupled to gravity. We also find that the entropy of our black hole may be higher than the corresponding conformal black hole which indicates that our solution may be thermodynamically preferred.