Ricci collineation vectors in fluid space-times
- Department of Physics Division of Mechanics, Astronomy and Astrophysics University of Athens, Zografos, Athens, (Greece)
- Centre for Nonlinear Studies Department of Computational and Applied Mathematics, University of the Witwatersrand, P. O. Wits 2050, Johannesburg, (South Africa)
The properties of fluid space-times that admit a Ricci collineation vector (RCV) parallel to the fluid unit four-velocity vector {ital u}{sup {ital a}} are briefly reviewed. These properties are expressed in terms of the kinematic quantities of the timelike congruence generated by {ital u}{sup {ital a}}. The cubic equation derived by Oliver and Davis (Ann. Inst. Henri Poincare {bold 30}, 339 (1979)) for the equation of state {ital p}={ital p}({mu}) of a perfect fluid space-time that admits an RCV, which does not degenerate to a Killing vector, is solved for physically realistic fluids. Necessary and sufficient conditions for a fluid space-time to admit a spacelike RCV parallel to a unit vector {ital n}{sup {ital a}} orthogonal to {ital u}{sup {ital a}} are derived in terms of the expansion, shear, and rotation of the spacelike congruence generated by {ital n}{sup {ital a}}. Perfect fluid space-times are studied in detail and analogues of the results for timelike RCVs parallel to {ital u}{sup {ital a}} are obtained. Properties of imperfect fluid space-times for which the energy flux vector {ital q}{sup {ital a}} vanishes and {ital n}{sup {ital a}} is a spacelike eigenvector of the anisotropic stress tensor {pi}{sub {ital ab}} are derived. Fluid space-times with anisotropic pressure are discussed as a special case of imperfect fluid space-times for which {ital n}{sup {ital a}} is an eigenvector of {pi}{sub {ital ab}}.
- OSTI ID:
- 6846703
- Journal Information:
- Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:7; ISSN JMAPA; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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