Skip to main content
SpringerLink
Log in

Contributions to the relativistic mechanics of continuous media

  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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)].

    Google Scholar 

  2. Lichnerowicz, A. (1955).Théories relativistes de la gravitation et de l'électromagnétisme (Masson, Paris).

    Google Scholar 

  3. Synge, J. L. (1937).Proc. Lond. Math. Soc. 43.

  4. Salzman, G., and Taub, A. H. (1954).Phys. Rev. 95, 1659.

    Google Scholar 

  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)].

    Google Scholar 

  7. Foures-Bruhat, Y. (1958).Comptes Rend. Acad. Sci. (Paris) II 246, 3319.

    Google Scholar 

  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. 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. Rayner, C. B. (1959).Comptes Rend. Acad. Sci. (Paris) II 248, 929, 2725;249, 1327.

    Google Scholar 

  11. Pirani, F. A. E. (1957).Phys. Rev. 105, 1089.

    Google Scholar 

  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.

    Google Scholar 

  14. Robertson, H. P. (1933).Rev. Mod. Phys. 5, 62.

    Google Scholar 

  15. Bondi, H. (1960).Cosmology (Cambridge University Press, Cambridge).

    Google Scholar 

  16. Einstein, A. (1949).The Meaning of Relativity (3rd. ed., Princeton University Press, Princeton).

    Google Scholar 

  17. Gödel, K. (1949).Rev. Mod. Phys. 21, 447.

    Google Scholar 

  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. 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. Eckart, C. (1940).Phys. Rev. 58, 919.

    Google Scholar 

  21. Meixner, J., and Reik, W. (1959). InHandbuch der Physik III, 2 (Springer-Verlag, Berlin).

    Google Scholar 

  22. Just, K. (1958). Habilitation Thesis, FU Berlin.

  23. Birkhoff, G. (1950). Hydrodynamics (Princeton University Press, Princeton).

    Google Scholar 

  24. Eisenhart, L. P. (1924).Trans. Amer. Math. Soc. 26, 205.

    Google Scholar 

  25. Jordan, P. (1955).Schwerkraft und Weltall (2nd. ed., Vieweg & Sohn, Braunschweig).

    Google Scholar 

  26. Fierz, M. (1956).Helv. Phys. Act. 29, 128.

    Google Scholar 

  27. Heckmann, O., and Schücking, E. (1959). InHandbuch der Physik LIII, 519 (??, Berlin).

    Google Scholar 

  28. Pirani, F. A. E. (1956).Acta Phys. Polonica 15, 389.

    Google Scholar 

  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. Whittaker, E. T. (1935).Proc. Roy. Soc. Lond. 149, 384.

    Google Scholar 

  31. Bondi, H., Pirani, F. A. E., and Robinson, I. (1959).Proc. Roy. Soc. Lond. A251, 519.

    Google Scholar 

  32. Witten L., ed. (1962).The Theory of Gravitation: An Introduction to Current Research (Wiley, New York).

    Google Scholar 

  33. Sasaki, M. (1958). InMax Planck Festschrift (VEB Deutscher Verlag der Wissenschaften, Berlin).

    Google Scholar 

  34. Grad, H. (1949).Comm. Pure Appl. Math. 2, 331.

    Google Scholar 

  35. Synge, J. L. (1960).Relativity: The General Theory (North-Holland, Amsterdam).

    Google Scholar 

  36. Grad, H. (1959). InHandbuch der Physik XII (Springer-Verlag, Berlin).

    Google Scholar 

  37. Taub, A. H. (1948).Phys. Rev. 74, 328.

    Google Scholar 

  38. Taub, A. H. (1956).Phys. Rev. 103, 454.

    Google Scholar 

  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. Heckmann, O. (1942).Theorien der Kosmologie (Springer-Verlag, Berlin).

    Google Scholar 

  41. Heckmann, O., and Schücking, E. (1955).Z. Ap. 38, 95 (I); (1956).40, 81 (II).

    Google Scholar 

  42. Tolman, R. C. (1934).Relativity, Thermodynamics and Cosmology (Oxford University Press, Oxford) [also reprinted (1987). (Dover, New York)].

    Google Scholar 

  43. Pound, R. V., and Rebka, G. A. (1960).Phys. Rev. Lett. 4, 337.

    Google Scholar 

  44. Raychaudhuri, A. (1955).Phys. Rev. 98, 1123.

    Google Scholar 

  45. Komar, A. (1956).Phys. Rev. 104, 544.

    Google Scholar 

  46. Eisenhart, L. P. (1956).Riemannian Geometry Princeton University Press, Princeton).

    Google Scholar 

  47. Ehlers, J. (1957). Dissertation, Hamburg University.

  48. Bondi, H. (1947).Mon. Not. R. Astr. Soc. 107, 410.

    Google Scholar 

  49. Kundt, W. (1955). Diploma Thesis, Hamburg University.

  50. Kundt, W. (1956).Z. Phys. 145, 611.

    Google Scholar 

  51. Einstein, A. (ed. P. A. Schilpp) (1949).Albert Einstein: Philosopher-Scientist (Library of Living Philosophers, Tudor, New York).

    Google Scholar 

  52. Ehlers, J. (1959). InLes Théories relativistes de la gravitation (Actes du Colloque Int., Royaumont, 21–27 Juin 1959) (CNRS, Paris).

    Google Scholar 

  53. Ehlers, J. (1962). InRecent Developments in General Relativity (Dedicated to Infeld) (Pergamon Press, Oxford, and PWN-Polish Scientific Publishers, Warsaw).

    Google Scholar 

  54. van Stockum, W. J. (1937).Proc. R. Soc. Edinburgh 57, 135.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max Planck Institute for Astrophysics, 85740, Garching-bei-München, Germany

    Jürgen Ehlers

Authors
  1. Jürgen Ehlers
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ehlers, J. Contributions to the relativistic mechanics of continuous media. Gen Relat Gravit 25, 1225–1266 (1993). https://doi.org/10.1007/BF00759031

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00759031

Keywords

Search

Navigation