Scattering of straight cosmic strings by black holes: Weak-field approximation

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Abstract
The scattering of a straight, infinitely long string moving with velocity upsilon 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 similar to -2 pi GM upsilon gamma/c(3)-pi(GM)(2)/(4c(3)upsilon b(imp)), where gamma=[1-(upsilon/c)(2)](-1/2). The second term dominates at low velocities upsilon/c<(GM/b(imp))(1/2). The late-time solution is represented by a kink and antikink, 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. [S0556-2821(98)02920-8].
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