Irrotational perfect fluids with a purely electric Weyl tensor

Details Irrotational perfect fluids with a purely electric Weyl tensor Irrotational perfect fluids with a purely electric Weyl tensor

Jul 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cqgra...6..949b&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 6, July 1, 1989, p. 949-960.

Statistics

Computation

47

Computational Astrophysics, Ideal Fluids, Potential Flow, Rotating Fluids, Tensors, Eigenvectors, Einstein Equations, Field Theory (Physics), Space-Time Functions

Scientific paper

All perfect fluid spacetimes with a purely electric Weyl tensor are shown to have an alignment between the fluid 4-velocity and a canonical null tetrad determined by the Weyl tensor. If, in addition, it is assumed that the flow is irrotational, the eigenframes of the shear and Weyl tensors coincide. In all but two rather special cases, it is proved that the vectors of this eigenframe are hypersurface orthogonal and consequently that a coordinate system exists in which the metric, shear and E(ab) (the electric part of the Weyl tensor) are all diagonal. Geodesic Petrov type D spacetimes are shown to be either Bianchi type 1 or to belong to the class of solutions considered by Szekeres and Szafron.

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