Interaction of a brane with a moving bulk black hole

We study 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 especially analyze applications to brane world models. We calculate the induced geometry on the brane generated by a moving black hole. From the point of view of a brane observer, this geometry can be obtained by solving (n+1)-dimensional Einstein's equations with a nonvanishing right-hand side. We calculate the effective stress-energy tensor corresponding to this "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.