Parallel waves in Einstein-nonlinear sigma models

Abstract

We study a family of solutions of Einstein-nonlinear sigma models with S2 and SU(2)∼S3 target manifolds. In the S2 case, the solutions are smooth everywhere, are free of conical singularities, and approach asymptotically the metric of a cosmic string, with a mass per length that is proportional to the absolute value of the winding number from topological spheres onto the target S2. This gives an interesting example of a relation between a mass and a topological charge. The case with target SU(2) generalizes the stationary solution found in Canfora et al.Eur. Phys. J. C 81, 55 (2021)EPCFFB1434-604410.1140/epjc/s10052-021-08854-x to parallel waves with a nonplanar wave front W. We prove that these W-fronted parallel waves are subquadratic in the classification in Flores et al.Classical Quantum Gravity 20, 2275 (2003)CQGRDG0264-938110.1088/0264-9381/20/11/322 and thus are causally well behaved. These spacetimes have a nonvanishing baryon current and their geometry has many striking features.