Ricci collineation vectors in fluid space-times

Journal Article · Sun Jul 01 04:00:00 EDT 1990 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.528668· OSTI ID:6846703

Tsamparlis, M ^[1]; Mason, D P ^[2]

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1. Department of Physics Division of Mechanics, Astronomy and Astrophysics University of Athens, Zografos, Athens, (Greece)
2. 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

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
DOCUMENT TYPES
EIGENVECTORS
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
FLUIDS
REVIEWS
RICCI TENSOR
SPACE-TIME
STRESSES
TENSORS
VECTORS