Averaging from a global point of view
Masayuki Tanimoto
Abstract
We study the averaging problem from a point of view of variation of spatial volume V. We show that in the space of spherically symmetric dust solutions which are regular on the spatial manifold S3 the variation δV vanishes at the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution in an appropriate sense, which supports the validity of the FLRW solution as the averaged solution. We also present the second variation δ2 V, giving the leading effect of the deviation from the FLRW solution.
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