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

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Abstract

We consider solutions of the Einstein field equations for which the Weyl tensor is of Petrov typeD, and whose source is a perfect fluid with equation of statep=p(w), wherep andw are the energy density and pressure of the fluid, respectively. We also impose two additional restrictions which are satisfied by most of the known solutions, namely, that the fluid 4-velocityu 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 tou. Our main result is that for this class of solutions, the equation of state satisfies eitherdp/dw=0 ordp/dw= 1, or else the solution admits three or more Killing vector fields.

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Author notes

  1. J. Carminati

    Present address: School of Mathematics and Computing, Western Australian Institute of Technology, 6102, Bentley, W.A., Australia

Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, N2L3G1, Waterloo, Ontario, Canada

    J. Carminati & J. Wainwright

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  1. J. Carminati
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  2. J. Wainwright
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Carminati, J., Wainwright, J. Perfect-fluid space-times with type-D Weyl tensor. Gen Relat Gravit 17, 853–867 (1985). https://doi.org/10.1007/BF00773682

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