Mathematics – Logic
Scientific paper
Jan 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980apj...235..307d&link_type=abstract
Astrophysical Journal, Part 1, vol. 235, Jan. 15, 1980, p. 307-334. Research supported by the National Research Council of Cana
Mathematics
Logic
39
Cosmology, Electromagnetic Fields, Magnetohydrodynamics, Relativity, Astronomical Models, Canonical Forms, Einstein Equations, Maxwell Equation, Tetrad Theory
Scientific paper
The purpose of this article is to investigate cosmological models satisfying the general relativistic field equations for electromagnetic field and perfect fluid, with particular reference to the nature of the 4-current. The investigation is concerned with tilting models as well as those whose 4-velocity is of the comoving form, and it is shown how the 'canonical tetrad', i.e., the tetrad with respect to which the energy-momentum tensor takes its canonical form, can be used to solve the problem of the possible forms of the 4-velocity. After a discussion of the canonical tetrad components of the general 4-current, including both convection and conduction currents, the Maxwell equations in spatially homogeneous cosmological models of types I, II, and III are solved and the resulting 4-current in each case is compared with the general expression found earlier for the 4-current. In most cases it is found that the 4-current is either spacelike or zero and the conductivity is finite. The results are illustrated by finding all solutions of the combined Einstein-Maxwell perfect fluid field equations in which the metric functions are powers of t. All of these solutions necessarily have spacelike or zero 4-current and finite conductivity.
Dunn K. A.
Tupper Brian O. J.
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