We prove that all spherically symmetric static spacetimes which are both regular at r = 0 and satisfying the single energy condition ρ + pr + 2pt ≥ 0 cannot contain any black hole region (equivalently, they must satisfy 2m/r ≤ 1 everywhere). This result holds even when the spacetime is allowed to contain a finite number of matching hypersurfaces. This theorem generalizes a result by Baumgarte a...

In the context of brane cosmology, a scenario where our universe is a 3 + 1dimensional surface (the “brane”) embedded in a five-dimensional spacetime (the “bulk”), we study geometries for which the brane is anisotropic — more specifically Bianchi I — though still homogeneous. We first obtain explicit vacuum bulk solutions with anisotropic three-dimensional spatial slices. The bulk is assumed to...