Abstract
Einstein's field equations are studied under the assumptions that (1) the source of the gravitational field is a perfect fluid, and (2) there exists a group of motions simply transitive on three-surfaces orthogonal to the fluid flow vector. There are two classes of solutions; these are studied in detail. Three special families of solutions examined include all analytic solutions of the field equations obeying (1) and (2) of which the authors are aware. The relation of these solutions to various vacuum solutions is indicated.
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References
Ellis, G. F. R.: J. Math. Phys.8, 1171 (1967).
Stewart, J. M., andG. F. R. Ellis: J. Math. Phys.9, 1072 (1968).
Ehlers, J.: Akad. Wiss. Lit. (Mainz), Abhandl. Math.-Nat. Kl. No. 11 (1961).
Eisenhart, L. P.: Continuous groups of transformations. New York: Dover 1961.
Taub, A. H.: Ann. Math.53, 472 (1951).
Heckmann, O., andE. Schücking: Solvay Conference Report. Brussels: Edition Stoops 1958; and Chap. 11 of Gravitation: An introduction to current research, ed.L. Witten, New York: Wiley 1962.
Gödel, K.: Proc. Intern. Congr. Math., Cambridge, Mass.1, 175 (1952).
Bianchi, L.: Lezioni sulla teoria dei gruppi continui finiti transformazioni. Pisa: Spoerri 1918.
Ellis, G. F. R.: Ph. D. Thesis, Cambridge University (1964).
Estabrook, F. B., H. D. Wahlquist, andC. G. Behr: J. Math. Phys.9, 497 (1968).
Misner, C. W.: Astrophys. J.151, 431 (1968).
Behr, C. G.: Z. Astrophys.54, 268 (1962), and Astron. Abhandl. Hamburg Sternwarte VII, 5 (1965).
Shepley, L.: Proc. Natl. Acad. Sci. U.S.52, 1403 (1964) and Ph. D. Thesis, Princeton University (1967).
Saunders, P. T.: Ph. D. Thesis, King's College, London University (1967).
Hawking, S. W.: Monthly Notices Roy. Astron. Soc.142, 129 (1969).
——, andG. F. R. Ellis: Phys. Letters17, 246 (1965).
Raychaudhuri, A.: Phys. Rev.98, 1123 (1955).
Estabrook, F. B., andH. D. Wahlquist: J. Math. Phys.5, 1629 (1964);7, 894 (1966), and JPL Tech. Rpt 32-868, Caltech. (1966).
Schücking, E.: Hamburg Relativity Seminar (1962);W. Kundt: Hamburg Relativity Seminar (1963);C. G. Behr, unpublished.
Jordan, P., J. Ehlers, andW. Kundt: Akad. Wiss. Lit. (Mainz), Abhandl. Math.-Nat. Kl. No. 7 (1960).
Sandage, A.: J. Soc. Ind. Appl. Math.10, 781 (1962).
Petrov, A. Z.: Einstein-Räume (transl.H.-J. Treder). Berlin: Akad. Verlag 1964.
Raychaudhuri, A.: Proc. Phys. Soc. (London)73, 263 (1958).
Robinson, B. B.: Proc. Natl. Acad. Sci. U.S.47, 1852 (1961).
Thorne, K. S.: Astrophys. J.148, 51 (1967).
Doroshkevich, A. S.: Astrophysics1, 138 (1965).
Jacobs, K. C.: Astrophys. J.153, 661 (1968).
Kasner, E.: Am. J. Math.43, 217 (1921).
Dautcourt, G., A. Papapetrou andH. Treder: Ann. Physik9, 330 (1962)
Misner, C. W.: Preprint, University of Maryland (1968).
Joseph, V.: Proc. Cambridge Phil. Soc.62, 87 (1966).
Kantowski, R., andR. K. Sachs: J. Math. Phys.7, 443 (1966).
— Ph. D. Thesis, University of Texas (1966).
Grishchuk, L. P.: Soviet Astron.-A. J.11, 881 (1968); Russian orig., Astron. Zh.44, 1097 (1967).
Ehlers, J., andW. Kundt: Chap. 2 of Gravitation: An introduction to current research, ed.L. Witten. New York: Wiley 1962.
Defrise, L.: Acad. Roy. Belg., Bull. classe Sci.53, 827 and 1276 (1967).
Newman, E. T., T. Unti, andL. A. Tamburino: J. Math. Phys.4, 915 (1963).
Misner, C. W.: J. Math. Phys.4, 924 (1963); and in: Relativity theory and astrophysics. Volume I, ed.J. Ehlers, Rhode Island, A.M.S. (1967). —Misner, C. W., andA. H. Taub: J.E.T.P.55, 233 (1968) in Russian.
Carter, B.: Phys. Letters26 A, 399 (1968).
Collinson, C. D., andD. C. French: J. Math. Phys.8, 701 (1967).
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Ellis, G.F.R., MacCallum, M.A.H. A class of homogeneous cosmological models. Commun.Math. Phys. 12, 108–141 (1969). https://doi.org/10.1007/BF01645908
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DOI: https://doi.org/10.1007/BF01645908