Interaction of a brane with a moving bulk black hole

TL;DR

This paper analyzes how an n-brane interacts with a moving higher-dimensional black hole, deriving perturbation equations, and exploring the induced geometry and apparent energy condition violations from a brane observer's perspective.

Contribution

It provides analytical solutions for brane-black hole interactions, calculates the induced geometry, and investigates apparent energy condition violations in brane world models.

Findings

Regions with apparent violation of energy conditions on the brane.

Explicit calculation of the induced geometry due to a moving black hole.

Analysis of light deflection caused by shadow matter.

Abstract

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 specially 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 non-vanishing 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'.