On the static solutions in gravity with massive scalar field in three dimensions

TL;DR

This paper explores static, circularly symmetric solutions in three-dimensional gravity with a massive scalar field, focusing on numerical integration under asymptotic flatness, revealing naked singularities and reviewing massless cases with cosmological constant.

Contribution

It provides the first numerical analysis of static solutions with a massive scalar field in 3D gravity, highlighting the absence of black holes and the presence of naked singularities.

Findings

Black holes do not exist in these solutions.

Naked singularities are present under asymptotic flatness.

Brief review of massless scalar field solutions with cosmological constant.

Abstract

We investigate circularly symmetric static solutions in three-dimensional gravity with a minimally coupled massive scalar field. We integrate numerically the field equations assuming asymptotic flatness, where black holes do not exist and a naked singularity is present. We also give a brief review on the massless cases with cosmological constant.