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A List of References on Spacetime Splitting and Gravitoelectromagnetism
Revised version to be published in the Proceedings of the Encuentros
Relativistas Espa\~noles, September, 2000 [ http://hades.eis.uva.es/EREs2000 ]Comment: 22 pages, LaTeX article style. Please send corrections and additions
to mailto:[email protected]
Stationary spacetimes and the Simon tensor
For stationary vacuum spacetimes the Bianchi identities of the second kind
equate the Simon tensor to the Simon-Mars tensor, the latter having a clear
geometrical interpretation. The equivalence of these two tensors is broken in
the nonvacuum case by additional source energy-momentum terms, but absorbing
these source terms into a redefinition of the Simon tensor restores the
equality. Explicit examples are discussed for electrovacuum and rigidly
rotating matter fields.Comment: To appear on the Proceedings of the International Conference in Honor
of Y. Choquet-Bruhat, "Analysis, Manifolds, and Geometric Structures in
Physics" Hotel Cala di Mola Porto Azzurro - Isola d'Elba June 24th-26th, 200
Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes
Stationary axisymmetric spacetimes containing a pair of oppositely-rotating
periodically-intersecting circular geodesics allow the study of various
so-called `clock effects' by comparing either observer or geodesic proper time
periods of orbital circuits defined by the observer or the geodesic crossing
points. This can be extended from a comparison of clocks to a comparison of
parallel transported vectors, leading to the study of special elements of the
spacetime holonomy group. The band of holonomy invariance found for a dense
subset of special geodesic orbits outside a certain radius in the static case
does not exist in the nonstatic case. In the Kerr spacetime the dimensionless
frequencies associated with parallel transport rotations can be expressed as
ratios of the proper and average coordinate periods of the circular geodesics.Comment: 23 pages latex(2e) iopart style, with 1 pictex figure and 2 eps
figure
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