Black holes in the brane world: Some exact solutions

We briefly review methods for and results from constructing multidimensional solutions with an event horizon generated by matter localized on a brane. We investigate a particular exact solution of the black star type with the Schwarzschild–Tangherlini geometry in the bulk. We study the extrinsic curvature tensor, which predicts the matter distribution on the brane in accordance with the Israel conditions. We calculate all components of the four-dimensional Riemann tensor describing the intrinsic geometry on the brane surface and also investigate their asymptotic forms at a large distance from the center, limits on the horizon, and the asymptotic forms in the singularity neighborhood of a five-dimensional black hole in the case where the brane intersects it.