The Constraint Equations

Details The Constraint Equations The Constraint Equations

2004-05-17

arxiv.org/abs/gr-qc/0405092v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages, LaTeX, to appear in the proceedings of the 2002 Cargese meeting "50 Years of the Cauchy Problem, in honour of Y. Cho

Scientific paper

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.

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