Existence and uniqueness of solutions of the Hamiltonian constraint of general relativity on compact manifolds
- 1 November 1973
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 14 (11) , 1551-1557
- https://doi.org/10.1063/1.1666225
Abstract
The Hamiltonian constraint ``G00 = 8πT00'' of general relativity is written as a quasilinear elliptic differential equation for the conformal factor of the metric of a three-dimensional spacelike manifold. It is shown that for ``almost every'' configuration of initial data on a compact manifold, with or without boundary, a solution exists. Dirichlet boundary conditions are assumed if the boundary is not empty. The solution is unique.This publication has 8 references indexed in Scilit:
- Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial-value problem of general relativityJournal of Mathematical Physics, 1973
- Structure of the Gravitational Field at Spatial InfinityJournal of Mathematical Physics, 1972
- Role of Conformal Three-Geometry in the Dynamics of GravitationPhysical Review Letters, 1972
- Mapping onto Solutions of the Gravitational Initial Value ProblemJournal of Mathematical Physics, 1972
- Gravitational Degrees of Freedom and the Initial-Value ProblemPhysical Review Letters, 1971
- Coordinate Invariance and Energy Expressions in General RelativityPhysical Review B, 1961
- Energy and the Criteria for Radiation in General RelativityPhysical Review B, 1960
- On the positive definite mass of the Bondi-Weber-Wheeler time-symmetric gravitational wavesAnnals of Physics, 1959