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Invariance of Positive-Frequency Kernels in Generalized FRW Spacetimes

Ph. Droz-Vincent
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Abstract

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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Ph. Droz-Vincent. 1998-01-05. Invariance of Positive-Frequency Kernels in Generalized FRW Spacetimes. https://arxiv.org/abs/gr-qc/9801007

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