Space-time averages in macroscopic gravity and volume-preserving coordinates.

Details Space-time averages in macroscopic gravity and volume-preserving coordinates. Space-time averages in macroscopic gravity and volume-preserving coordinates.

Sep 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jmp....38.4741m&link_type=abstract

Journal of Mathematical Physics, Vol. 38, No. 9, p. 4741 - 4757

Mathematics

Mathematical Physics

23

Space-Time: Gravitation Theory

Scientific paper

The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski space-time is given and comparison between this averaging scheme and that adopted in macroscopic gravity is carried out. Some new results concerning the algebraic structure of the averaging operator are precisely formulated and proved. The previously proved existence theorems for the averaging and coordination bilocal operators are revisited with more detailed proofs of related results. A number of new results concerning the structure of the volume-preserving averaging operators and the class of proper coordinate systems are given.

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