(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>)-dimensional black holes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> gravity

Abstract

We consider a $f(R)$ gravity theory in ($2+1$)-dimensions with a self-interacting scalar field nonminimally coupled to gravity. Without specifying the form of the $f(R)$ function, solving the field equations we find that the Ricci scalar receives a nonlinear correction term which breaks the conformal invariance and leads to a massless black hole solution. When the nonlinear 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.

Topics & Concepts