Conformally dressed black hole in 2+1 dimensions

TL;DR

This paper presents a new three-dimensional black hole solution with a conformal scalar field, analyzing its geometric, thermodynamic properties, and singularities, contributing to understanding scalar fields in lower-dimensional gravity.

Contribution

It introduces a novel static, circularly symmetric black hole solution in 2+1 dimensions coupled to a conformal scalar field, with unique thermodynamic characteristics.

Findings

Scalar field is regular everywhere

Entropy is two-thirds of the standard value

Temperature fixed by regularity at the horizon

Abstract

A three dimensional black hole solution of Einstein equations with negative cosmological constant coupled to a conformal scalar field is given. The solution is static, circularly symmetric, asymptotically anti-de Sitter and nonperturbative in the conformal field. The curvature tensor is singular at the origin while the scalar field is regular everywhere. The condition that the Euclidean geometry be regular at the horizon fixes the temperature to be $T=\frac{9\, r_+}{16\pi l^2}$. Using the Hamiltonian formulation including boundary terms of the Euclidean action, the entropy is found to be $\frac{2}{3}$ of the standard value ($\frac{1}{4} A$), and in agreement with the first law of thermodynamics.