Shear-free perfect fluids with zero magnetic Weyl tensor
Rotating, shear-free general-relativistic perfect fluids are investigated. It is first shown that, if the fluid pressure, p, and energy density, ..mu.., are related by a barotropic equation of state p = p( ..mu..) satifying ..mu..+pnot =0, and if the magnetic part of the Weyl tensor (with respect to the fluid flow) vanishes, then the fluid's volume expansion is zero. The class of all such fluids is subsequently characterized. Further analysis of the solutions shows that, in general, the space-times may be regarded as being locally stationary and axisymmetric (they admit a two-dimensional Abelian isometry group with timelike orbits, which is in fact orthogonally transistive), although various specializations can occur, with the ''most special'' case being the well-known Goedel model, which is space-time homogeneous (it admits a five-dimensional isometry group acting multiply transitively on the space-time). all solutions are of Petrov type D. The fact that there are any solutions in the class at all means that a theorem appearing in the literature is invalid, and the existence of some special solutions in which the fluid's vorticity vector is orthogonal to the acceleration reveals the incompleteness of a previous study of a class of space-times, in which there are Killing vectors parallel to the fluid four-velocity and to the vorticity vector.
- Research Organization:
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3Gl Canada
- OSTI ID:
- 5168706
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 25:4; ISSN JMAPA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
EQUATIONS
EQUATIONS OF STATE
FIELD THEORIES
FLUID FLOW
FLUIDS
GENERAL RELATIVITY THEORY
IDEAL FLOW
SHEAR
TENSORS
UNIFIED-FIELD THEORIES
WEYL UNIFIED THEORY