General Relativity and Gravitation

, Volume 25, Issue 12, pp 1225–1266 | Cite as

Contributions to the relativistic mechanics of continuous media

  • Jürgen Ehlers
Golden Oldie


This is a translation from German of an article originally published inProceedings of the Mathematical-Natural Science Section of the Mainz Academy of Science and Literature, Nr. 11, 1961 (pp. 792–837) (printed by Franz Steiner and Co, Wiesbaden), 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.


Exact Solution General Relativity Apply Mathematic Field Equation Differential Geometry 
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  1. 1.
    Landau, L. D., and Lifschitz, E. M. (1962)The Classical Theory of Fields (Addison-Wesley, Reading, Mass.) [also reprinted (1975). (Pergamon Press, Oxford)].Google Scholar
  2. 2.
    Lichnerowicz, A. (1955).Théories relativistes de la gravitation et de l'électromagnétisme (Masson, Paris).Google Scholar
  3. 3.
    Synge, J. L. (1937).Proc. Lond. Math. Soc. 43.Google Scholar
  4. 4.
    Salzman, G., and Taub, A. H. (1954).Phys. Rev. 95, 1659.Google Scholar
  5. 5.
    Jordan, P., Ehlers, J., Sachs, R. K. (1961).Akad. Wiss. Mainz. Abh. math.-nat. Kl. 1961 Nr. 1.Google Scholar
  6. 6.
    Synge, J. L., and Schild, A. (1952).Tensor Calculus (University of Toronto Press, Toronto) [also reprinted (1978). (Dover, New York)].Google Scholar
  7. 7.
    Foures-Bruhat, Y. (1958).Comptes Rend. Acad. Sci. (Paris) II 246, 3319.Google Scholar
  8. 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.Google Scholar
  9. 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).Google Scholar
  10. 10.
    Rayner, C. B. (1959).Comptes Rend. Acad. Sci. (Paris) II 248, 929, 2725;249, 1327.Google Scholar
  11. 11.
    Pirani, F. A. E. (1957).Phys. Rev. 105, 1089.Google Scholar
  12. 12.
    Jordan, P., Ehlers, J., and Kundt, W. (1960).Akad. Wiss. Mainz. Abh. math.-nat. Kl. 1961 Nr. 2.Google Scholar
  13. 13.
    Just, K. (1956).Z. Physik. 145, 235.Google Scholar
  14. 14.
    Robertson, H. P. (1933).Rev. Mod. Phys. 5, 62.Google Scholar
  15. 15.
    Bondi, H. (1960).Cosmology (Cambridge University Press, Cambridge).Google Scholar
  16. 16.
    Einstein, A. (1949).The Meaning of Relativity (3rd. ed., Princeton University Press, Princeton).Google Scholar
  17. 17.
    Gödel, K. (1949).Rev. Mod. Phys. 21, 447.Google Scholar
  18. 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)].Google Scholar
  19. 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)].Google Scholar
  20. 20.
    Eckart, C. (1940).Phys. Rev. 58, 919.Google Scholar
  21. 21.
    Meixner, J., and Reik, W. (1959). InHandbuch der Physik III, 2 (Springer-Verlag, Berlin).Google Scholar
  22. 22.
    Just, K. (1958). Habilitation Thesis, FU Berlin.Google Scholar
  23. 23.
    Birkhoff, G. (1950). Hydrodynamics (Princeton University Press, Princeton).Google Scholar
  24. 24.
    Eisenhart, L. P. (1924).Trans. Amer. Math. Soc. 26, 205.Google Scholar
  25. 25.
    Jordan, P. (1955).Schwerkraft und Weltall (2nd. ed., Vieweg & Sohn, Braunschweig).Google Scholar
  26. 26.
    Fierz, M. (1956).Helv. Phys. Act. 29, 128.Google Scholar
  27. 27.
    Heckmann, O., and Schücking, E. (1959). InHandbuch der Physik LIII, 519 (??, Berlin).Google Scholar
  28. 28.
    Pirani, F. A. E. (1956).Acta Phys. Polonica 15, 389.Google Scholar
  29. 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)].Google Scholar
  30. 30.
    Whittaker, E. T. (1935).Proc. Roy. Soc. Lond. 149, 384.Google Scholar
  31. 31.
    Bondi, H., Pirani, F. A. E., and Robinson, I. (1959).Proc. Roy. Soc. Lond. A251, 519.Google Scholar
  32. 32.
    Witten L., ed. (1962).The Theory of Gravitation: An Introduction to Current Research (Wiley, New York).Google Scholar
  33. 33.
    Sasaki, M. (1958). InMax Planck Festschrift (VEB Deutscher Verlag der Wissenschaften, Berlin).Google Scholar
  34. 34.
    Grad, H. (1949).Comm. Pure Appl. Math. 2, 331.Google Scholar
  35. 35.
    Synge, J. L. (1960).Relativity: The General Theory (North-Holland, Amsterdam).Google Scholar
  36. 36.
    Grad, H. (1959). InHandbuch der Physik XII (Springer-Verlag, Berlin).Google Scholar
  37. 37.
    Taub, A. H. (1948).Phys. Rev. 74, 328.Google Scholar
  38. 38.
    Taub, A. H. (1956).Phys. Rev. 103, 454.Google Scholar
  39. 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)].Google Scholar
  40. 40.
    Heckmann, O. (1942).Theorien der Kosmologie (Springer-Verlag, Berlin).Google Scholar
  41. 41.
    Heckmann, O., and Schücking, E. (1955).Z. Ap. 38, 95 (I); (1956).40, 81 (II).Google Scholar
  42. 42.
    Tolman, R. C. (1934).Relativity, Thermodynamics and Cosmology (Oxford University Press, Oxford) [also reprinted (1987). (Dover, New York)].Google Scholar
  43. 43.
    Pound, R. V., and Rebka, G. A. (1960).Phys. Rev. Lett. 4, 337.Google Scholar
  44. 44.
    Raychaudhuri, A. (1955).Phys. Rev. 98, 1123.Google Scholar
  45. 45.
    Komar, A. (1956).Phys. Rev. 104, 544.Google Scholar
  46. 46.
    Eisenhart, L. P. (1956).Riemannian Geometry Princeton University Press, Princeton).Google Scholar
  47. 47.
    Ehlers, J. (1957). Dissertation, Hamburg University.Google Scholar
  48. 48.
    Bondi, H. (1947).Mon. Not. R. Astr. Soc. 107, 410.Google Scholar
  49. 49.
    Kundt, W. (1955). Diploma Thesis, Hamburg University.Google Scholar
  50. 50.
    Kundt, W. (1956).Z. Phys. 145, 611.Google Scholar
  51. 51.
    Einstein, A. (ed. P. A. Schilpp) (1949).Albert Einstein: Philosopher-Scientist (Library of Living Philosophers, Tudor, New York).Google Scholar
  52. 52.
    Ehlers, J. (1959). InLes Théories relativistes de la gravitation (Actes du Colloque Int., Royaumont, 21–27 Juin 1959) (CNRS, Paris).Google Scholar
  53. 53.
    Ehlers, J. (1962). InRecent Developments in General Relativity (Dedicated to Infeld) (Pergamon Press, Oxford, and PWN-Polish Scientific Publishers, Warsaw).Google Scholar
  54. 54.
    van Stockum, W. J. (1937).Proc. R. Soc. Edinburgh 57, 135.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Jürgen Ehlers
    • 1
  1. 1.Max Planck Institute for AstrophysicsGarching-bei-MünchenGermany

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