Gravitational capture and scattering of straight test strings with large impact parameters

The capture or scattering of an initially straight infinite test cosmic string by a Kerr-Newman black hole, or by any other small source of an electrovac gravitational field, is analyzed analytically when the string moves with initial velocity v₀ and large impact parameter z₀=b≫M so that the string stays very nearly straight (except during the final capture process, if that occurs, or except far behind the gravitating object, if b≫/M/√1-v₀²). The critical impact parameter for capture at low velocities, v₀≪1-Q²/M², is shown to be b_crit=√(π/2)(M²-Q²)/v₀+O(M). For all b>b_crit, the displacement of the string from the plane of the gravitating object after the scattering approaches the final value z_f≈√b²-(π/2)(M²-Q²)/v₀-2πMv₀/√1-v₀², for any v₀, as long as b≫M.