Scattering of Straight Cosmic Strings by Black Holes: Weak Field Approximation

TL;DR

This paper analyzes how an infinitely long cosmic string is scattered by a black hole in the weak gravitational field, deriving exact solutions and describing the resulting string displacement and phase change.

Contribution

It provides exact solutions for cosmic string scattering by black holes in the weak field approximation, including displacement and phase change analysis.

Findings

Displacement of string proportional to black hole mass and velocity

Late-time solutions involve kink and anti-kink propagations

Comparison with numerical results confirms analytical solutions

Abstract

The scattering of a straight, infinitely long string moving with velocity $v$ by a black hole is considered. We analyze the weak-field case, where the impact parameter ($b_{imp}$) is large, and obtain exact solutions to the equations of motion. As a result of scattering, the string is displaced in the direction perpendicular to the velocity by an amount $\Delta b\sim -2\pi GMv\gamma/c^3 -\pi (GM)^2/ (4c^3 v b_{imp})$, where $\gamma=(1-(v/c)^2)^{-1/2}$. The second term dominates at low velocities $v/c<(GM/b_{imp})^{1/2}$ . The late-time solution is represented by a kink and anti-kink, propagating in opposite directions at the speed of light, and leaving behind them the string in a new ``phase''. The solutions are applied to the problem of string capture, and are compared to numerical results.