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 6 M/ √ 1− v2 0 ). The critical impact parameter for capture at low velocities, v0 1−Q2/M2, is shown to be bcrit = √ (π/2)(M2 −Q)/v0 + O(M). For all b > bcrit, the displacement of the string from the plane of the gravitating object after the scattering approaches the final value zf ≈ √ b2 − (π/2)(M2 −Q)/v0 −2πMv0/ √ 1− v2 0 , for any v0, so long as b M . ∗Alberta-Thy-05-98, gr-qc/9804088 †Internet address: [email protected]