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

TL;DR

This paper analytically investigates how straight cosmic strings are captured or scattered by Kerr-Newman black holes at large impact parameters, deriving critical impact parameters and displacement formulas.

Contribution

It provides new analytical expressions for the critical impact parameter and string displacement after scattering by a black hole with charge and rotation.

Findings

Critical impact parameter for capture at low velocities derived.

Displacement of string after scattering approximated for large impact parameters.

Analytical formulas applicable to Kerr-Newman black holes and similar sources.

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.