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

Jean-Pierre De Villiers·Valeri Frolov
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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 $Δb\sim -2πGMvγ/c^3 -π(GM)^2/ (4c^3 v b_{imp})$, where $γ=(1-(v/c)^2)^{-1/2}$. 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.

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Jean-Pierre De Villiers, Valeri Frolov. 1998-04-30. Scattering of Straight Cosmic Strings by Black Holes: Weak Field Approximation. https://doi.org/10.1103/physrevd.58.105018

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