Thick de Sitter 3-branes, dynamic black holes, and localization of gravity

The embedding of a thick de Sitter 3-brane into a five-dimensional bulk is studied, assuming a scalar field with a potential is present in the bulk. A class of solutions is found in closed form that can represent a thick de Sitter 3-brane interpolating either between two dynamical black holes with an R×S₄ topology or between two Rindler-like spacetimes with an R₂×S₃ topology. The gravitational field is localized in a small region near the center of the 3-brane. The analysis of graviton fluctuations shows that a zero mode exists and separates itself from a set of continuous modes by a mass gap. The existence of such a mass gap is shown to be universal. The scalar perturbations are also studied and shown to be stable.