The York map is a canonical transformation
type: Item
instance of: scholarly article
title: The York map is a canonical transformation
zbMATH Open document ID: 0589.53071
DOI: 10.1016/0393-0440(84)90015-9
author: J. E. Marsden
author: James Isenberg
published in: Journal of Geometry and Physics
publication date: 1984-01-01T00:00:00Z
review text: A fundamental object of study in the Einstein theory of gravity is the York map, which in the vacuum case is a map from the freely chosen conformal data (i.e. pairs (3-metric, transverse traceless, conjugate momentum)) to the space of constraint satisfying physical data (analogously for the vacuum case). Introduced in a Hamiltonian context, the question of whether the York map is a symplectic one or not naturally arises. This work demonstrates that the York map is a degenerate symplectic map, the domain and range of which are presymplectic varieties. Passing to suitable quotients, a nondegenerate York map between symplectic varieties is obtained.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 83C05
zbMATH DE Number: 3947138
zbMATH Keywords: symplectic geometry
zbMATH Keywords: Einstein equation
zbMATH Keywords: Einstein-Maxwell theory
zbMATH Keywords: York map
zbMATH Keywords: symplectic map
zbMATH Keywords: presymplectic varieties
MaRDI profile type: Publication
full work available at URL: 0393-0440(84)90015-9
OpenAlex ID: W2037987651
cites work: Q5613138
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cites work: Reduction of symplectic manifolds with symmetry
cites work: Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial-value problem of general relativity
description: scientific article; zbMATH DE number 3947138