×

Contributions to the relativistic mechanics of continuous media. (English) Zbl 0792.53070

Summary: This is a translation from German of an article originally published in Proceedings of the Mathematical-Natural Science Section of the Mainz Academy of Science and Literature [see: Strenge Lösungen der Feldgleichungen der allgemeinen Relativitätstheorie. IV: Beiträge zur relativistischen Mechanik kontinuierlicher Medien, Akad. Wiss. Lit. Mainz, Abh. Math.-Naturwiss. Kl. 1961, 793-837 (1961; Zbl 0116.215)], which is Paper IV in the series “Exact Solutions of the Field Equations of General Relativity Theory” by Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt and Rainer K. Sachs. The translation has been carried out by G. F. R. Ellis (Department of Applied Mathematics, University of Cape Town), assisted by P. K. S. Dunsby, so that this outstanding review paper can be readily accessible to workers in the field today. As far as possible, the translation has preserved both the spirit and the form of the original paper. Despite its age, it remains one of the best reviews available in this area.

MSC:

53Z05 Applications of differential geometry to physics
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory

Citations:

Zbl 0116.215
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Landau, L. D., and Lifschitz, E. M. (1962)The Classical Theory of Fields (Addison-Wesley, Reading, Mass.) [also reprinted (1975). (Pergamon Press, Oxford)]. · Zbl 0178.28704
[2] Lichnerowicz, A. (1955).Théories relativistes de la gravitation et de l’électromagnétisme (Masson, Paris). · Zbl 0065.20704
[3] Synge, J. L. (1937).Proc. Lond. Math. Soc. 43.
[4] Salzman, G., and Taub, A. H. (1954).Phys. Rev. 95, 1659. · Zbl 0056.43805 · doi:10.1103/PhysRev.95.1659
[5] Jordan, P., Ehlers, J., Sachs, R. K. (1961).Akad. Wiss. Mainz. Abh. math.-nat. Kl. 1961 Nr. 1.
[6] Synge, J. L., and Schild, A. (1952).Tensor Calculus (University of Toronto Press, Toronto) [also reprinted (1978). (Dover, New York)]. · Zbl 0038.32301
[7] Foures-Bruhat, Y. (1958).Comptes Rend. Acad. Sci. (Paris) II 246, 3319.
[8] Gödel, K. (1952). InProc. Int. Congress of Mathematicians (Cambridge, Mass., Aug./Sept. 1950), (Int. Congress Mathematicians/A.M.S., Providence, R.I.) vol. 1.
[9] Schücking, E., and Heckmann, O. (1959). InOnzième Conseil de Physique Solvay: La Structure et l’Évolution de l’Univers, Int. Inst. de Physique Solvay (Editions Stoop, Brussels).
[10] Rayner, C. B. (1959).Comptes Rend. Acad. Sci. (Paris) II 248, 929, 2725;249, 1327.
[11] Pirani, F. A. E. (1957).Phys. Rev. 105, 1089. · Zbl 0077.41901 · doi:10.1103/PhysRev.105.1089
[12] Jordan, P., Ehlers, J., and Kundt, W. (1960).Akad. Wiss. Mainz. Abh. math.-nat. Kl. 1961 Nr. 2.
[13] Just, K. (1956).Z. Physik. 145, 235. · doi:10.1007/BF01339058
[14] Robertson, H. P. (1933).Rev. Mod. Phys. 5, 62. · Zbl 0006.23105 · doi:10.1103/RevModPhys.5.62
[15] Bondi, H. (1960).Cosmology (Cambridge University Press, Cambridge). · Zbl 0046.20807
[16] Einstein, A. (1949).The Meaning of Relativity (3rd. ed., Princeton University Press, Princeton). · Zbl 0033.42501
[17] Gödel, K. (1949).Rev. Mod. Phys. 21, 447. · Zbl 0041.56701 · doi:10.1103/RevModPhys.21.447
[18] Weyl, H. (1921/1923/1970/1988).Raum Zeit Materie (4th ed., 5th ed., 6th ed., 7th ed., Springer-Verlag, Berlin) [English transl. reprinted (1952).Space-Time-Matter (Dover, New York)]. · JFM 48.0984.01
[19] Pauli, W. (1921). ?Relativitätstheorie? InEnzykl. d. Math. Wiss. (Teubner, Leipzig) vol. 5, part 2, p. 539 [English transl. with supplements (1958).Theory of Relativity (Pergamon Press, London/Oxford)]. · JFM 18.0124.02
[20] Eckart, C. (1940).Phys. Rev. 58, 919. · Zbl 0027.03107 · doi:10.1103/PhysRev.58.919
[21] Meixner, J., and Reik, W. (1959). InHandbuch der Physik III, 2 (Springer-Verlag, Berlin).
[22] Just, K. (1958). Habilitation Thesis, FU Berlin.
[23] Birkhoff, G. (1950). Hydrodynamics (Princeton University Press, Princeton). · Zbl 0041.53903
[24] Eisenhart, L. P. (1924).Trans. Amer. Math. Soc. 26, 205. · JFM 50.0596.03 · doi:10.1090/S0002-9947-1924-1501273-1
[25] Jordan, P. (1955).Schwerkraft und Weltall (2nd. ed., Vieweg & Sohn, Braunschweig). · Zbl 0065.20703
[26] Fierz, M. (1956).Helv. Phys. Act. 29, 128.
[27] Heckmann, O., and Schücking, E. (1959). InHandbuch der Physik LIII, 519 (??, Berlin).
[28] Pirani, F. A. E. (1956).Acta Phys. Polonica 15, 389.
[29] Fock, V. (1960).Theorie von Raum, Zeit und Gravitation (Akademie-Verlag, Berlin) [English transl. by N. N. Kemmer (1964).The Theory of Space, Time and Gravitation (2nd. rev. ed., Macmillan, New York)].
[30] Whittaker, E. T. (1935).Proc. Roy. Soc. Lond. 149, 384. · Zbl 0011.37702 · doi:10.1098/rspa.1935.0069
[31] Bondi, H., Pirani, F. A. E., and Robinson, I. (1959).Proc. Roy. Soc. Lond. A251, 519. · Zbl 0084.44002 · doi:10.1098/rspa.1959.0124
[32] Witten L., ed. (1962).The Theory of Gravitation: An Introduction to Current Research (Wiley, New York). · Zbl 0115.43103
[33] Sasaki, M. (1958). InMax Planck Festschrift (VEB Deutscher Verlag der Wissenschaften, Berlin).
[34] Grad, H. (1949).Comm. Pure Appl. Math. 2, 331. · Zbl 0037.13104 · doi:10.1002/cpa.3160020403
[35] Synge, J. L. (1960).Relativity: The General Theory (North-Holland, Amsterdam). · Zbl 0090.18504
[36] Grad, H. (1959). InHandbuch der Physik XII (Springer-Verlag, Berlin).
[37] Taub, A. H. (1948).Phys. Rev. 74, 328. · Zbl 0035.12103 · doi:10.1103/PhysRev.74.328
[38] Taub, A. H. (1956).Phys. Rev. 103, 454. · Zbl 0074.22201 · doi:10.1103/PhysRev.103.454
[39] Boltzmann, L. (1895).Vorlesungen über Gastheorie (Barth, Leipzig) [English transl. by S. G. Brush (1964).Lectures on Gas Theory (University of California Press, Berkeley)].
[40] Heckmann, O. (1942).Theorien der Kosmologie (Springer-Verlag, Berlin). · JFM 68.0635.04
[41] Heckmann, O., and Schücking, E. (1955).Z. Ap. 38, 95 (I); (1956).40, 81 (II).
[42] Tolman, R. C. (1934).Relativity, Thermodynamics and Cosmology (Oxford University Press, Oxford) [also reprinted (1987). (Dover, New York)]. · Zbl 0009.41304
[43] Pound, R. V., and Rebka, G. A. (1960).Phys. Rev. Lett. 4, 337. · doi:10.1103/PhysRevLett.4.337
[44] Raychaudhuri, A. (1955).Phys. Rev. 98, 1123. · Zbl 0066.22204 · doi:10.1103/PhysRev.98.1123
[45] Komar, A. (1956).Phys. Rev. 104, 544. · Zbl 0072.21402 · doi:10.1103/PhysRev.104.544
[46] Eisenhart, L. P. (1956).Riemannian Geometry Princeton University Press, Princeton).
[47] Ehlers, J. (1957). Dissertation, Hamburg University.
[48] Bondi, H. (1947).Mon. Not. R. Astr. Soc. 107, 410.
[49] Kundt, W. (1955). Diploma Thesis, Hamburg University.
[50] Kundt, W. (1956).Z. Phys. 145, 611. · doi:10.1007/BF01332282
[51] Einstein, A. (ed. P. A. Schilpp) (1949).Albert Einstein: Philosopher-Scientist (Library of Living Philosophers, Tudor, New York).
[52] Ehlers, J. (1959). InLes Théories relativistes de la gravitation (Actes du Colloque Int., Royaumont, 21-27 Juin 1959) (CNRS, Paris).
[53] Ehlers, J. (1962). InRecent Developments in General Relativity (Dedicated to Infeld) (Pergamon Press, Oxford, and PWN-Polish Scientific Publishers, Warsaw).
[54] van Stockum, W. J. (1937).Proc. R. Soc. Edinburgh 57, 135.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.