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

100%

Szczyrba W.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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Lagrangian formalism in the classical field theory

43%

Szczyrba W.

Annales Polonici Mathematici

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1976

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tom 32

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nr 2

145-185

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Differentiation in locally convex spaces

31%

Szczyrba W.

Studia Mathematica

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1971

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tom 39

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nr 3

289-306

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

3 Szczyrba W.

1 1977

1 1976

1 1971

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

Lagrangian formalism in the classical field theory

Differentiation in locally convex spaces