HAMILTONIAN APPROACH TO RELATIVISTIC STAR MODELS

An ADM-like Hamiltonian approach is proposed for static spherically sy mmetric relativistic star configurations. For a given equation of stat e the entire information about the model can be encoded in a certain t wo-dimensional minisuperspace geometry. We derive exact solutions whic h arise from symmetries corresponding to linear and quadratic geodesic invariants in minisuperspace by exploiting the relation to minisupers pace Killing tensors. A classification of exact solutions having the f ull number of integration constants is given according to their minisu perspace symmetry properties. In particular it is shown that Schwarzsc hild's exterior solution and Buchdahl's n = 1 polytrope solution corre spond to minisuperspaces with a Killing vector symmetry, while Schwarz schild's interior solution, Whittaker's solution and Buchdahl's n = 5 polytrope solution correspond to minisuperspaces with a second rank Ki lling tenser. New solutions filling in empty slots in this classificat ion scheme are also given. One of these new solutions has a physically reasonable equation of state and is a generalization of Buchdahl's n = 1 polytrope model.