Séminaires sur les aspects théoriques et expérimentaux de la gravitation

Hyperbolicity of constrained Hamiltonian systems

by Prof. David HILDITCH (University of Jena)

Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)

Amphithéâtre Léon Motchane

Institut des Hautes Etudes Scientifiques

Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette
Motivated by the question, "what coordinates choices are `good' for general relativity?" I will discuss gauge theories from the from the free evolution point of view, in which initial data satisfying constraints of a theory are given, and because the constraints are compatible with the field equations they remain so. I will present a model constrained Hamiltonian theory and identify a particular structure in the equations of motion from which statements can be made about the status of the initial value problem, just by examining a subset of the equations, called the pure gauge subsystem. I will then present the application of these ideas to GR, which results in a five parameter generalization of the `good' gauge used in Choquet-Bruhat's original treatment of the initial value problem.