Physics
Scientific paper
Aug 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gregr..14..717t&link_type=abstract
General Relativity and Gravitation, vol. 14, Aug. 1982, p. 717-725.
Physics
2
Conducting Fluids, Field Theory (Physics), Interstellar Magnetic Fields, Relativity, Rotating Fluids, Einstein Equations, Gravitational Fields, Lines Of Force, Maxwell Equation, Riemann Manifold
Scientific paper
It is investigated whether expressions for the vorticity along a magnetic field line are valid for a fluid with finite electric conductivity in the same way as Ferraro's law is true in general. The Ricci identity for the four-velocity field is used, and a mathematical identity for the vorticity along a magnetic field line is derived in terms of the Riemann curvature tensor and the kinematic quantities. The result is valid for a fluid with finite, even nonuniform, electric conductivity as well as for an infinitely conducting fluid. Two special cases are considered, the Weyl tensor and Einstein's gravitational field equations are introduced, and the role played by the free gravitational field and the gravitational field determined locally by the energy distribution is examined.
Mason P. D.
Tsamparlis Michael
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