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On the geometric structure of the set of solutions of Einstein equations

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Rozprawy Matematyczne tom/nr w serii: 150 wydano: 1977
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Abstrakty
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CONTENTS

1. Introduction .......................................................................................................................................................... 5
2. Notation and preliminary remarks............................................................................................................................ 7
3. A geometric approach to the calculus of variations............................................................................................... 9
4. Multisymplectic manifolds and a multiphase structure of a classical field theory........................................... 19
5. A multiphase structure of General Relativity............................................................................................................ 22
6. The Cauchy problem and ADMW coordinates in General Relativity................................................................... 26
7. A symplectic structure in the set of solutions of field equations.......................................................................... 29
8. A symplectic structure in the set of Einstein metrics.............................................................................................. 36
9. The gauge distribution and the action of the diffeomorphism group.................................................................. 39
10. Degrees of freedom and a superphase space -for General Relativity............................................................. 46
11. A pseudo-differential structure in the space ℋ. A Lie algebra of functionals on ℋ....................................... 48
12. A variational principle for General Relativity............................................................................................................ 55
13. The Hamilton-Jacobi equation in lagrangian field theories................................................................................ 57
14. The Hamilton-Jacobi equation in General Relativity............................................................................................. 62
15. Proofs............................................................................................................................................................................. 66
Appendix. Proof of the ellipticity of the operator AA*..................................................................................................... 79
References.......................................................................................................................................................................... 82
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 150
Liczba stron
83
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae CL
Daty
wydano
1977
Twórcy
Bibliografia
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