A nonsingular spacetime defect

Abstract

A nonsingular localized static classical solution is constructed for standard Einstein gravity coupled to an $SO(3)\ifmmode\times\else\texttimes\fi{}SO(3)$ chiral model of scalars (Skyrme model). This solution corresponds to a spacetime defect and its construction proceeds in three steps. First, an 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.