Shear‐free normal cosmological models are the perfect fluid solutions of Einstein’s equations in which rotation and shear vanish, and which are not static [they were all found by A. Barnes, Gen. Relativ. Gravit. 4, 105 (1973)]. They are either spherically, plane, or hyperbolically symmetric. Their symmetries are discussed in various coordinate systems and related to the conformal group of the three‐dimensional flat space. A coordinate representation is introduced which unites all three cases into a single two‐parameter family. The limiting transitions to the Friedman–Lemaitre–Robertson–Walker (FLRW) models and to the Schwarzschild–de Sitter‐like solutions are presented.
REFERENCES
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A. Krasiński, in Proceedings of the 4th Marcel Grossman Meeting on General Relativity, edited by R. Ruffini (Elsevier, Amsterdam, 1986), p. 989.
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12.
References 10 and 11 discussed the Barnes models, in particular the plane symmetric one, even though no mention of Barnes’s paper was made there.
13.
G. F. R. Ellis, in General Relativity and Gravitation, edited by B. Bertotti, F. de Felice, and A. Pascolini (Reidel, Dordrecht, 1984), p. 215.
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For mysterious reasons, the solution obtained in Ref. 17 is now commonly called “the Tolman‐Bondi model” or “the Tolman model” although Tolman (Ref. 19) quoted Lemaitre (Ref. 17) and Bondi (Ref. 20) quoted Tolman (Ref. 19), none of them claiming priority.
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These formulas were calculated by the algebraic program ORTOCARTAN (see also Refs. 23–25).
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A. Krasiński, in International Conference on Computer Algebra and its Applications in Theoretical Physics, edited by N. N. Govorun (Joint Institute for Nuclear Research, Dubna, 1986), p. 50.
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A. Krasiński and M. Perkowski, The System ORTOCARTAM—User’s Manual (University of Cologne, Cologne, 1983), 3rd ed. (available as a magnetic tape recording or a printout).
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D. Kramer, H. Stephani, E. Herlt, and M. A. H. MacCallum, Exact Solutions of Einstein’s Field Equations (Cambridge U.P., Cambridge, 1980), pp. 103 and 104.
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1989
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