Mathematics
Scientific paper
Mar 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cqgra...2..229v&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 2, March 1, 1985, p. 229-240. Research supported by the Fonds National de l
Mathematics
4
Axes Of Rotation, Gravitation Theory, Rotating Matter, Space-Time Functions, Unified Field Theory, Cosmic Dust, Energy Transfer, Minkowski Space, Momentum Transfer, Singularity (Mathematics), Tensor Analysis
Scientific paper
A set of 'extended' regularity conditions is discussed which have to be satisfied on the rotation axis if the latter is assumed to be also an axis of symmetry. For a wide class of energy-momentum tensors these conditions can only hold at the origin of the Weyl canonical coordinate. For static and cylindrically symmetric space-times the conditions can be derived from the regularity of the Riemann tetrad coefficients on the axis. For stationary space-times, however, the extended conditions do not necessarily hold, even when 'elementary flatness' is satisfied and when there are no curvature singularities on the axis. The result by Davies and Caplan (1971) for cylindrically symmetric stationary Einstein-Maxwell fields is generalized by proving that only Minkowski space-time and a particular magnetostatic solution possess a regular axis of rotation. Further, several sets of solutions for neutral and charged, rigidly and differentially rotating dust are discussed.
van den Bergh Norbert
Wils Patrick
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