The initial value problem and the dynamical formulation of general relativity

A discussion is presented of some of the inter-relationships between the initial value problem, the canonical formalism, linearization stability and the space gravitational degrees of freedom. The first section develops the Hamiltonian formalism for the dynamics of general relativity. The study of the constraint manifold follows. Existence, uniqueness and stability for the Cauchy problem is then discussed. Conditions are given under which first-order perturbation theory is and is not valid. The last section discusses the elimination of gauges by a general reduction procedure for Hamiltonian systems. An application of this general procedure is then used to show that the space of gravitational degrees of freedom is generically an infinite-dimensional symplectic manifold. (U.K.)