Isotropy and Stability of the Brane

We reexamine Wald's no-hair theorem for global anisotropy in the brane world scenarios. We derive a set of sufficient conditions which must be satisfied by the brane matter and bulk metric so that a homogeneous and anisotropic brane asymptotically evolves to a de Sitter spacetime in the presence of a positive cosmological constant on the brane. We discuss the violations of these sufficient conditions and we show that a negative nonlocal energy density or the presence of strong anisotropic stress (i.e., a magnetic field) may lead the brane to collapse. We discuss the generality of these conditions.