Exact hairy black holes asymptotically $AdS_{2+1}$

TL;DR

This paper introduces a family of asymptotically $AdS_{2+1}$ hairy black holes within Einstein's scalar field theory, analyzing their thermodynamics and phase structure using boundary conditions, superpotential, and regularization methods.

Contribution

It constructs and analyzes new asymptotically $AdS_{2+1}$ hairy black hole solutions, including thermodynamic properties and phase behavior, within Einstein's minimally coupled scalar field framework.

Findings

Derived the boundary conditions and superpotential for the solutions.

Calculated free energy and Brown-York tensor using two regularization methods.

Analyzed thermodynamic phases and stability of the black holes.

Abstract

We present a family of $AdS_{2+1}$ 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.