# General Black Hole Solutions in (2+1)-dimensions with a Scalar Field Non-Minimally Coupled to Gravity

## TL;DR

This paper derives a general class of black hole solutions in (2+1)-dimensional gravity with a non-minimally coupled scalar field, unifying known solutions and discovering new ones, including asymptotically AdS and de Sitter black holes.

## Contribution

It provides a general solution framework for (2+1)-dimensional black holes with scalar fields non-minimally coupled to gravity, encompassing known solutions and introducing new exact and numerical solutions.

## Key findings

- Includes all known asymptotically AdS black holes as special cases.
- Derives new exact AdS black hole solutions for specific coupling constants.
- Finds numerical solutions and discusses potential de Sitter black holes.

## Abstract

We discuss black hole solutions in (2+1)-dimensions with a scalar field non-minimally coupled to Einstein's gravity in the presence of a cosmological constant and a self-interacting scalar potential. Without specifying the form of the potential, we find a general solution of the field equations, which includes all the known asymptotically anti-de Sitter (AdS) black hole solutions in (2+1)-dimensions as special cases once values of the coupling constants are chosen appropriately. In addition, we obtain numerically new black hole solutions and for some specific choices of the coupling constants we derive new exact AdS black hole solutions. We also discuss the possibility of obtaining asymptotically de Sitter black hole solutions with or without an electromagnetic field.