Gravitational Capture and Scattering of Straight Test Strings with Large Impact Parameters

Abstract

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 and large impact parameter 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 is not much greater than the energy of the object in the frame of the string). The critical impact parameter for capture at low velocities is shown to be [(pi/2)(M^2-Q^2)/v]^{1/2}. For all larger b, the displacement of the string from the plane of the gravitating object after the scattering approaches the final value [b^2 - (pi/2)(M^2-Q^2)/v]^{1/2} - 2 pi M v/(1-v^2)^{1/2}, for any v, so long as b >> M.