  In this work, we obtain isotropic extensions of the usual spherically
symmetric vacuum geometries in general relativity. Exact and perturbative
solutions are derived. The classes of geometries obtained include black holes
in compact and noncompact universes, wormholes in the interior region of
cosmological horizons, and anti-de Sitter geometries with excess/deficit solid
angle. The tools developed here are applicable in more general contexts.
