The York Map is a canonical transformation

Isenberg, J. and J. E. Marsden

J. Geom. Phys., 1, (1984), 85-105

Abstract:

The York mapping from the space of freely chosen conformal data to the space of constraint-satisfying physical data is shown to be a canonical transformation for both the vacuum Einstein theory and the Einstein-Maxwell theory.
This paper is entirely directed toward proving that the York map is symplectic: We define the important spaces of fields and their reductions, describe the York map, establish its properties, show that ti reduces properly. and then state and prove the result. We do this first for the vacuum Einstein theory and then for the Einstein-Maxwell equations. Some applications of the results herein to other connections between the conformal and ADM pictures are planned for a future publication.