Tomimatsu-Sato solutions describe cosmic strings interacting with gravitational waves

We demonstrate that the proper place of the Tomimatsu-Sato solutions is in the description of cylindrically symmetric spacetimes, as opposed to stationary axisymmetric spacetimes. More particularly, we consider a version of the δ=2 Tomimatsu-Sato solutions, obtained from the standard Tomimatsu-Sato solutions by an analytic continuation, that describe a cylindrically symmetric spacetime. It admits a regular axis, is asymptotically flat, and is smooth everywhere but the axis where it exhibits a conical, but not a curvature, singularity. The spacetime describes a beam-like-shaped pulse of gravitational radiation scattered by a cosmic string