Rotating hairy black hole and its microscopic entropy in three spacetime dimensions

We present a spinning hairy black hole in gravity minimally coupled to a self-interacting real scalar field in three spacetime dimensions. The black hole is characterized by having a single horizon that encloses a curvature singularity and the scalar field is regular everywhere. The mass and angular momentum are shown to be finite. The presence of a scalar field with a slower falloff at infinity leads an anti-de Sitter asymptotic behavior that differs from the one found by Brown and Henneaux but has the same symmetry group as in pure gravity. A scalar soliton, which is a finite mass regular solution devoid of integration constants, plays the role of the ground state. The existence of this soliton is the key to deriving the semiclassical entropy of the rotating hairy black hole using the counting of microscopic states provided by the Cardy formula.