Nonsingular, lump-like, scalar compact objects in $(2+1)$-dimensional Einstein gravity

TL;DR

This paper explores exact solutions in (2+1)-dimensional Einstein gravity coupled with a scalar field, identifying nonsingular, lump-like compact objects that could have astrophysical relevance in higher dimensions.

Contribution

It classifies scalar field solutions in (2+1)D gravity, highlighting a branch with nonsingular, lump-like compact objects and analyzing their geometric properties.

Findings

Identified a family of scalar Lagrangians with exact solutions

Discovered solutions that are either naked singularities or nonsingular objects

Nonsingular solutions are localized, lump-like, and have a boundary unreachable by geodesics

Abstract

We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions in static and circularly symmetric scenarios, we classify the various types of solutions and focus on a branch that yields asymptotically flat geometries. We show that the solutions within such a branch can be divided in two types, namely, naked singularities and nonsingular objects without a center. In the latter, the energy density is localized around a maximum and vanishes only at infinity and at an inner boundary. This boundary has vanishing curvatures and cannot be reached by any time-like or null geodesic in finite affine time. This allows us to consistently interpret such solutions as nonsingular, lump-like, static compact scalar objects, whose eventual extension to the $(3+1)$-dimensional context could provide structures of astrophysical interest.