Interaction of cosmic strings and branes with black holes.

摘要

In this thesis we investigate the interaction of cosmic strings and braves with black holes. First, the scattering of a straight, infinitely long cosmic string by a rotating black hole is considered. We assume that the string is moving with velocity υ, and it is initially parallel to the axis of rotation of the black hole. We demonstrate that as a result of scattering, the string is displaced in the direction perpendicular to the velocity by an amount κ(υ, b), where b is the, impact parameter. We present the results of a numerical study of string scattering and their comparison with a weak field approximation, and also with scattering by a non-rotating black hole which was studied in earlier works. Next we study critical scattering and capture of a cosmic string—we demonstrate that there exists a critical value of the impact parameter b_c(υ) which separates scattering from the capture regime. Using numerical simulations we obtain the critical impact parameter curve for different values of the rotation parameter α. We show that for the prograde motion of the string this curve lies below the curve for the retrograde motion. Moreover, for ultrarelativistic strings moving in the prograde direction and nearly extremal black holes the critical impact parameter curve is found to be a multiple valued function of υ. We also study the relativistic regime, especially such effects as coil formation and wrapping effect. Finally, we analyse the interaction of an n-dimensional topological defect (n-brane) described by the Nambu-Goto action with a higher-dimensional Schwarzschild black hole moving in the bulk spacetime. We derive the general form of the perturbation equations for an n-brane in the weak field approximation and solve them analytically in the most interesting cases. We specially analyze applications to brane world models. We calculate the induced geometry on the brane together with the effective stress-energy tensor corresponding to a ‘shadow-matter’. We explicitly show that there exist regions on the brane where a brane observer sees an apparent violation of energy conditions. We also study the deflection of light propagating in the region of influence of this ‘shadow matter’.