Hamiltonian structures for compact homogeneous universes

Details Hamiltonian structures for compact homogeneous universes Hamiltonian structures for compact homogeneous universes

1997-05-20

arxiv.org/abs/gr-qc/9705052v1

J.Math.Phys. 38 (1997) 6560-6577

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages including 2 figures. REVTeX and epsf packages

Scientific paper

10.1063/1.532225

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key ingredients of our arguments is a suitable mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variations, i.e., the covering group is fixed. We discuss general problems concerned with the use of this expression in the context of general relativity, and demonstrate the reduction of the Hamiltonians for some examples. For our models, all the dynamical degrees of freedom in Hamiltonian view are unambiguously interpretable as geometrical deformations, in contrast to the conventional open models.

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