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Three dimensional rotating hairy black holes, asymptotics and thermodynamics

A rotating hairy black hole solution is found in gravity minimally coupled to a self-interacting real scalar field in three spacetime dimensions. Then we discuss analytically the horizon structure and find an analogue of the famous Kerr bound in (2+1) dimensions because of the existence of black hole horizons. We present the asymptotic symmetries and find the same symmetry group (i.e. the conformal group) and central charge as in pure gravity. Based on the asymptotic behavior, the mass and angular momentum are presented by the Regge-Teitelboim approach. Other thermodynamic quantities are also obtained and the first law of black hole thermodynamics and Smarr relation are checked. In addition, we also investigate the local thermodynamic stability and find the existence of Hawking-Page phase transition in the rotating hairy black hole.