Brane cosmology and the self-tuning of the cosmological constant in the presence of bulk black holes

Motivated by the holographic self-tuning proposal of the cosmological constant, we generalize and study the cosmology of brane-worlds embedded in a higher-dimensional bulk black hole geometry. We describe the equations and matching conditions in the case of flat, spherical and hyperbolic slicing of the bulk geometry and find the conditions for the existence of a static solution. We solve the equations that govern dynamical geometries in the probe brane limit and we describe in detail the resulting brane-world cosmologies. Of particular interest are the properties of solutions when the brane-world approaches the black hole horizon. In this case the geometry induced on the brane is that of de Sitter, whose entropy and temperature is related to those of the higher dimensional bulk black hole.