Exact hairy black holes asymptotically $Ad{S}_{2+1}$

Abstract

We present a family of $Ad{S}_{2+1}$ asymptotically hairy black holes, within the context of Einstein's minimally coupled scalar field theory. We study the boundary conditions and construct the thermal superpotential. In the Euclidean section, we calculate the free energy and in the Lorentzian section, the Brown-York tensor, both regularized by two methods. Finally, we calculate the relevant thermodynamic quantities and analyze the different phases.