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 $v_0$ and large impact parameter $z_0=b\gg M$ 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 $b\gg /M/\sqrt{1-v_0^2}).\mathrm{}$ The critical impact parameter for capture at low velocities, $v_0\ll 1-Q^2{/M}^2,$ is shown to be $b_{\mathrm{crit}}=\sqrt{(\pi {/2\left)\right(M}^2-Q^2{)/v}_0}+O\left(M\right).$ For all $b>\mathrm{}{b}_{\mathrm{crit}},$ the displacement of the string from the plane of the gravitating object after the scattering approaches the final value $z_f\approx \sqrt{b^2-(\pi {/2\left)\right(M}^2-Q^2{)/v}_0}-2\pi {\mathrm{Mv}}_0/\sqrt{1-v_0^2},$ for any $v_0,$ as long as $b\gg M.\mathrm{}$