The Einstein Equations of Evolution-A Geometric Approach

DOI10.1063/1.1666014zbMath0233.58009OpenAlexW2165882997MaRDI QIDQ5641809

Jerrold E. Marsden, Arthur E. Fischer

Publication date: 1972

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1666014

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Equations in function spaces; evolution equations (58D25)

Related Items

A Riemannian generalization of a result of DeWitt concerning Ricci-flat Lorentz metrics, BV analysis of Polyakov and Nambu-Goto theories with boundary, Unnamed Item, Deformations of the embedded Einstein spaces, On the DeWitt metric, Infinite-dimensional Lie groups and algebras in mathematical physics, Conformal changes of metrics and the initial-value problem of general relativity, Some dynamical properties of Einstein space-times admitting a Gaussian foliation, Natural bundles. I. A minimal resolution of superspace, General relativity as a generalized Hamiltonian system, Solutions of Einstein's equations with conformal symmetries and a contact slice, Tetrads in SU(3) × SU(2) × U(1) Yang–Mills geometrodynamics, CLASSICAL AND QUANTUM FEATURES OF THE MIXMASTER SINGULARITY, Instability in superspace, GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY, Linearization stability of the Einstein equations, The existence of maximal slicings in asymptotically flat spacetimes, Global analysis and general relativity, A symplectic structure on the set of Einstein metrics. A canonical formalism for general relativity, Clebsch-Lagrange variational principle and geometric constraint analysis of relativistic field theories, A new Hamiltonian structure for the dynamics of general relativity, Perfect fluid sources for spatially homogeneous spacetimes, Remarks about the thin sandwich conjecture, Moduli spaces with external fields, A symplectic structure for the Einstein-Maxwell field, The dynamical degrees of freedom in spatially homogeneous cosmology, A multisymplectic description of the Einstein-generalized Born-Infeld theory, The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. I, Einstein's equations near spatial infinity, 4-D GEOMETRICAL MODELING OF MATERIAL AGING, Linearization stability of Einstein equations coupled with self-gravitating scalar fields, Linearization stability of the Einstein equation for Robertson–Walker models. I, Geometry of minisuperspace in examples, The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity, Laplacian in the hyperbolic space Hn and linearization stability of the Einstein equation for Robertson-Walker models, Diffusive inflationary cosmology

Cites Work

• Global aspects of the Cauchy problem in general relativity
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Feynman Quantization of General Relativity
• Dynamical Structure and Definition of Energy in General Relativity
• Quantum Theory of Gravity. I. The Canonical Theory