Black holes of $(2+1)$-dimensional $f(R)$ gravity coupled to a scalar field

Abstract

We consider $f(R)$ gravity theories in the presence of a scalar field minimally coupled to gravity with a self-interacting potential in $(2+1)$-dimensions. Without specifying the form of the $f(R)$ function, we first obtain an exact black hole solution dressed with scalar hair with the scalar charge to appear in the $f(R)$ function and we discuss its thermodynamics. This solution at large distances gives a hairy BTZ black hole, and it reduces to the BTZ black hole when the scalar field decouples. In a pure $f(R)$ gravity supported by the scalar field, we find an exact hairy black hole similar to the BTZ black hole with phantom hair and an analytic $f(R)$ form and discuss its thermodynamics.

arXiv commentReferences added, 15 pages, 6 figures, accepted for publication in PRD

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• Black Holes with Scalar Hair in Three Dimensions
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• Electromagnetic Generalized Quasi-topological gravities in $(2+1)$ dimensions
• New black hole solutions in three-dimensional $f(R)$ gravity
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• Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes