Regular black holes in three dimensions

TL;DR

This paper introduces new analytic black hole and horizonless solutions in three-dimensional gravity coupled with a scalar field, expanding the landscape of regular and singular spacetimes beyond the BTZ black hole.

Contribution

It presents a family of new three-dimensional black hole solutions with scalar fields, including regular, singular, and horizonless spacetimes, generalizing the BTZ black hole.

Findings

Some solutions are completely regular without singularities.

Solutions include black holes with multiple horizons and conical or BTZ-like singularities.

Certain solutions are globally regular and horizonless.

Abstract

We find a plethora of new analytic black holes and globally regular horizonless spacetimes in three dimensions. The solutions involve a single real scalar field $\phi$ which always admits a magnetic-like expression proportional to the angular coordinate. The new metrics, which satisfy $g_{tt}g_{rr}=-1$ and represent continuous generalizations of the BTZ one, solve the equations of Einstein gravity corrected by a new family of densities (controlled by unconstrained couplings) constructed from positive powers of $(\partial \phi)^2$ and certain linear combinations of $R^{ab} \partial_a \phi \partial_b \phi$ and $(\partial \phi)^2 R$. Some of the solutions obtained describe black holes with one or several horizons. A set of them possesses curvature singularities, while others have conical or BTZ-like ones. Interestingly, in some cases the black holes have no singularity at all, being completely regular. Some of the latter are achieved without any kind of fine tuning or constraint between the action parameters and/or the physical charges of the solution. An additional class of solutions describes globally regular and horizonless geometries.