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

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.

19 pages, 5 figures