Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-01-05
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages. Plain TeX file
Scientific paper
We consider the Klein-Gordon equation in FRW-like spacetimes, with compact space sections (not necessarily isotropic neither homogeneous). The bi-scalar kernel allowing to select the positive-frequency part of any solution is developed on mode solutions, using the eigenfunctions of the three-dimensional Laplacian. Of course this kernel is not unique but, except (perhaps) when the scale factor undergoes a special law of evolution, the metric has no more symmetries (connected with the identity) than those inherited from the space sections. As a result, all admissible definitions of the positive-frequency kernel are related one to another by a unitary transformation which commutes with the connected isometries of spacetime; any such kernel is invariant under these isometries isometries. A physical interpretation is tentatively suggested.
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