Parallel waves in Einstein-nonlinear sigma models

BEATRICE BONGA; GUSTAVO DOTTI

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2022

1550-7998

We study a family of solutions of Einstein-non linear sigma models with S^2 and SU(2) ∼ S^3target manifolds. In the S^2 case, the solutions are smooth everywhere, 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 S^2. This givesan interesting example of a relation between a mass and a topological charge. The case with targetSU(2) generalizes the stationary solution found in Eur. Phys. J. C (2021) 81:55 to parallel waveswith a non-planar wavefront W. We prove that these W-fronted parallel waves are sub-quadraticin the classification in Class. Quant. Grav. 20 (2003) 2275, and thus causally well behaved. Thesespacetimes have a non-vanishing baryon current and their geometry has many striking features.