Three Dimensional Gravity in the Presence of Scalar Fields

TL;DR

This paper explores three-dimensional gravity coupled with scalar fields, deriving a perturbative solution that is asymptotically exact and discusses how to handle singularities by excising problematic regions.

Contribution

It presents a new static perturbative solution for scalar fields in 3D gravity that is asymptotically exact and addresses singularity issues.

Findings

Solution is asymptotically exact at infinity

Curvature singularity occurs at the origin

Region near the singularity must be excised to avoid naked singularity

Abstract

We study a scalar field in curved space in three dimensions. We obtain a static perturbative solution and show that this solution satisfies the exact equations in the asymptotic region at infinity. The new solution gives rise to a singularity in the curvature scalar at the origin. Our solution, however, necessitates the excising the region near the origin, thus this naked singularity is avoided.