Irrotational perfect fluids with a purely electric Weyl tensor
Abstract
All perfect fluid spacetimes with a purely electric Weyl tensor are shown to have an alignment between the fluid 4velocity 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 July 1989
 DOI:
 10.1088/02649381/6/7/003
 Bibcode:
 1989CQGra...6..949B
 Keywords:

 Computational Astrophysics;
 Ideal Fluids;
 Potential Flow;
 Rotating Fluids;
 Tensors;
 Eigenvectors;
 Einstein Equations;
 Field Theory (Physics);
 SpaceTime Functions;
 Astrophysics