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Gravitational Pulse Wave Scattering and the Geroch group

Cylindrical gravitational pulse waves are cylindrical gravitational waves with a pulse profile in the radial direction. The dynamics of cylindrical gravitational pulse waves is governed by a two dimensional integrable sigma model with an infinite dimensional hidden symmetry called the Geroch group. Piran, Safier, and Katz obtained an exact solution for a single pulse wave by making a double analytic continuation of the Kerr metric. Their solution describes a pulse wave that arrives from infinity, bounces off the symmetry axis, and returns to infinity. In this note, we obtain an exact solution for a double pulse wave by making a double analytic continuation of the double Kerr metric. The new solution describes a pair of pulse waves that arrive from infinity, scatter through each other, and return to infinity. The pulses pass through each other and emerge with their shapes intact, as in ordinary soliton scattering. Unlike ordinary soliton scattering, there is no time delay. The metric is free of the conical singularity that appears in the double Kerr metric. In the future, it would be interesting to understand how the Geroch group manifests in the quantum version of gravitational pulse wave scattering.