Regular black holes in three dimensions

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 $\ensuremath{\phi}$ which always admits a magneticlike expression proportional to the angular coordinate. The new metrics, which satisfy ${g}_{tt}{g}_{rr}=\ensuremath{-}1$ and represent continuous generalizations of the Ba\~nados-Teitelboim-Zanelli (BTZ) one, solve the equations of Einstein gravity corrected by a new family of densities (controlled by unconstrained couplings) constructed from positive powers of $(\ensuremath{\partial}\ensuremath{\phi}{)}^{2}$ and certain linear combinations of ${R}^{ab}{\ensuremath{\partial}}_{a}\ensuremath{\phi}{\ensuremath{\partial}}_{b}\ensuremath{\phi}$ and $(\ensuremath{\partial}\ensuremath{\phi}{)}^{2}R$. 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.