An algorithm is presented for determining all solutions of the Einstein field equations representing a perfect fluid with metric of the form ds2=dt2−e2αdz2 −e2β(dx2+dy2) and fluid flow vector u=∂/∂t. The entire class of solutions is then invariantly characterized. These new solutions generalize Szekeres’ inhomogeneous cosmological models containing dust. A subclass of these solutions is studied in detail and it is interesting that some of these models approach isotropy but not homogeneity for large cosmological times.
REFERENCES
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P.
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D. A.
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4.
These equations were checked using the Camel computer programs of S. J. Campbell, M. Math. Thesis, University of Waterloo (1976).
5.
The metric is a surface of constant curvature See Ref. 1, Appendix.
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E. Kamke, Differentialgleichungen Losungsmethoden und Losungen (Akademische Verlagsgesellschaft Geest Portig K.‐H., Leipzig, 1961), Vol. 1, pp. 401–2.
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See Ref. 6.
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See Ref. 2.
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See, for example, G. F. R. Ellis, “General Relativity and Cosmology,” Proceedings of the International School of Physics Enrico Fermi, Course XLVII, edited by R. K. Sachs (Academic, New York, 1971).
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For definitions of these limits see Ref. 2.
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See Ref. 2.
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See Ref. 10, page 115.
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See Ref. 1, page 62.
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S. J. Campbell and J. Wainwright, “Symbolic Computation and the Newman—Penrose Formalism,” preprint, University of Waterloo (1976).
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© 1977 American Institute of Physics.
1977
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