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 $\mathrm{}(n+1\mathrm{})\mathrm{}$-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.