We discuss the properties of black holes in brane-world scenarios where our Universe is viewed as a four-dimensional sub-manifold of some higher-dimensional spacetime. We consider in detail such a model where four-dimensional spacetime lies at the junction of several domain walls in a higher dimensional anti–de Sitter spacetime. In this model there may be any number p of infinitely large extra dimensions transverse to the brane-world. We present an exact solution describing a black p-brane which will induce on the brane-world the Schwarzschild solution. This exact solution is unstable to the Gregory-Laflamme instability, whereby long-wavelength perturbations cause the extended horizon to fragment. We therefore argue that at late times a non-rotating uncharged black hole in the brane-world is described by a deformed event horizon in $p+4\mathrm{}$ dimensions which will induce, to good approximation, the Schwarzschild solution in the four-dimensional brane world. When $p=2,$ this deformed horizon resembles a black diamond and more generally for $p>\mathrm{}2,$ a polyhedron.

• Received 22 February 2000

DOI:https://doi.org/10.1103/PhysRevD.62.044012