The Constraint Equations
arXiv:gr-qc/0405092
Abstract
We review the properties of the constraint equations, from their geometric origin in hypersurface geometry through to their roles in the Cauchy problem and the Hamiltonian formulation of the Einstein equations. We then review properties of the space of solutions and construction techniques, including the conformal and conformal thin sandwich methods, the thin sandwich method, quasi-spherical and generalized QS methods, gluing techniques and the Corvino-Schoen projection.
34 pages, LaTeX, to appear in the proceedings of the 2002 Cargese meeting "50 Years of the Cauchy Problem, in honour of Y. Choquet-Bruhat", editors P.T.Chruściel and H. Friedrich
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Cited by in corpus (9)
- Initial boundary value problems for Einstein's field equations and geometric uniqueness
- A variational principle for stationary, axisymmetric solutions of Einstein's equations
- Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes
- Extreme Bowen-York initial data
- Cauchy problems for Lorentzian manifolds with special holonomy
- Scalar Curvature and the Einstein Constraint Equations
- The Yamabe invariant for axially symmetric two Kerr black holes initial data
- Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints
- Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary