CLASSIFYING EINSTEIN FIELD-EQUATIONS WITH APPLICATIONS TO COSMOLOGY AND ASTROPHYSICS

The field equations for spacetimes with finite-dimensional Hamiltonian dynamics are discussed. Examples of models belonging to this class ar e the cosmological spatially homogeneous models, the astrophysically i nteresting static spherically symmetric models, static cylindrically s ymmetric models, and certain cosmological self-similar models. A numbe r of different sources are considered. Although these models arise fro m quite different physical contexts, their field equations all share a common mathematical structure. This motivates a classification of Ein stein's field equations. Several classification schemes, based on prop erties under various variable transformations, are presented. It is sh own how these schemes can be used to classify dynamical properties of the models and how one can thereby obtain qualitative information. It is also shown how one scheme can be used in order to find symmetries a nd exact solutions.