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

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 Banados, Teitelboim, and Zanelli (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.