We investigate the evolution of small perturbations around black strings and branes which are low energy solutions of string theory. For simplicity we focus attention on the zero charge case and show that there are unstable modes for a range of time frequency and wavelength in the extra 10-D dimensions. These perturbations can be stabilized if the extra dimensions are compactified to a scale smaller than the minimum wavelength for which instability occurs and thus will not affect large astrophysical black holes in four dimensions. We comment on the implications of this result for the cosmic censorship hypothesis.

Starting from a completely general standpoint, we find the most general brane-Universe solutions for a three-brane in a five dimensional spacetime. The brane can border regions of spacetime with or without a cosmological constant. Making no assumptions other than the usual cosmological symmetries of the metric, we prove that the equations of motion form an integrable system, and find the exact solution. The cosmology is indeed a boundary of a (class II) Schwarzschild-AdS spacetime, or a Minkowski (class I) spacetime. We analyse the various cosmological trajectories focusing particularly on those bordering vacuum spacetimes. We find, not surprisingly, that not all cosmologies are compatible with an asymptotically flat spacetime branch. We comment on the role of the radion in this picture.

The standard picture of viable higher-dimensional theories is that direct manifestations of extra dimensions occur at short distances only, whereas long-distance physics is effectively four-dimensional. We show that this is not necessarily true in models with infinite extra dimensions. As an example, we consider a five-dimensional scenario with three 3-branes in which gravity is five dimensional at both short- and very long-distance scales, with conventional four-dimensional gravity operating at intermediate length scales. A phenomenologically acceptable range of validity of four-dimensional gravity extending from microscopic to cosmological scales is obtained without strong fine-tuning of parameters.