Perfect-fluid space-times with type-D Weyl tensor

Details Perfect-fluid space-times with type-D Weyl tensor Perfect-fluid space-times with type-D Weyl tensor

Sep 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985gregr..17..853c&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 17, Sept. 1985, p. 853-867.

Mathematics

8

Cosmology, Equations Of State, Ideal Fluids, Relativity, Space-Time Functions, Tensor Analysis, Einstein Equations, Vectors (Mathematics)

Scientific paper

Solutions of the Einstein field equations are considered, for which the Weyl tensor is of Petrov type D and whose source is a perfect fluid with equation of state p = p(w), where p and w are the energy density and pressure of the fluid, respectively. Two additional restrictions are imposed which are satisfied by most of the known solutions, namely, that the fluid 4-velocity u lies in the 2-space spanned by the two repeated principal null directions of the Weyl tensor, and that the Weyl tensor has zero magnetic part relative to u. The main result is that for this class of solutions, the equation of state satisfies either dp/dw = 0 or dp/dw = 1, or else the solution admits three or more Killing vector fields.

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