A nonsingular spacetime defect

TL;DR

This paper constructs a nonsingular, localized spacetime defect solution within Einstein gravity coupled to a Skyrme scalar model, demonstrating the theoretical possibility of nonsingular defects with nontrivial topology.

Contribution

It presents the first explicit construction of a nonsingular spacetime defect solution with nonsimply connected topology in Einstein-Skyrme theory.

Findings

Exact vacuum solution with nonsimply connected topology

Existence of a matter-coupled defect solution

Demonstration that nonsingular defects are theoretically possible

Abstract

A nonsingular localized static classical solution is constructed for standard Einstein gravity coupled to an $SO(3)\times SO(3)$ chiral model of scalars (Skyrme model). This solution corresponds to a spacetime defect and its construction proceeds in three steps. First, an \textit{Ansatz} is presented for a solution with nonsimply connected topology of the spacetime manifold. Second, an exact vacuum solution of the reduced field equations is obtained. Third, matter fields are included and a particular exact solution of the reduced field equations is found. The latter solution has a diverging total energy, but its existence at least demonstrates that a nonsingular defect-type solution having nonsimply connected topology is possible with nontrivial matter fields.