Exact hypersurface-homogeneous solutions in cosmology and astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies, and extends most known work on hypersurface-homogenous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, such as Brans-Dicke or higher-dimensional theories.