Advertisement

General Relativity and Gravitation

, Volume 14, Issue 3, pp 243–254 | Cite as

Variational formulation of general relativity from 1915 to 1925 “Palatini's method” discovered by Einstein in 1925

  • M. Ferraris
  • M. Francaviglia
  • C. Reina
Research Articles

Abstract

Among the three basic variational approaches to general relativity, the metric-affine variational principle, according to which the metric and the affine connection are varied independently, is commonly known as the “Palatini method.” In this paper we revisit the history of the “golden age” of general relativity, through a discussion of the papers involving a variational formulation of the field problem. In particular we find that the original Palatini paper of 1919 was rather far from what is usually meant by “Palatini's method,” which was instead formulated, to our knowledge, by Einstein in 1925.

Keywords

General Relativity Variational Principle Differential Geometry Variational Formulation Variational Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Misner, C. W., Thorne, K. S., and Wheeler, J. A., (1973).Gravitation. Freeman & Co., San Francisco.Google Scholar
  2. 2.
    Schrödinger, E. (1954).Space-Time Structure, 2nd ed. Cambridge University Press, Cambridge, England.Google Scholar
  3. 3.
    Narlikar, J. V. (1978).Lectures on General Relativity. MacMillan, London.Google Scholar
  4. 4.
    Palatini, A. (1919). Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton,Rend. Circ. Mat. Palermo,43, 203.Google Scholar
  5. 5.
    Einstein, A., and Grossmann, M. (1914). Kovarianzeigenschaften der Feldgleichungen der auf die verallgemeinerte Relativitätstheorie gegründeten Gravitationstheorie,Z. Math. Phys.,63, 215.Google Scholar
  6. 6.
    Lorentz, H. A. (1915). On Hamilton principle in Einstein's theory of gravitation,Versl. K. Akad. Wetensch. Amsterdam,23, 1073; (1915).Proc. Acad. Amsterdam,19, 751 (reprinted in H. A. Lorentz,Collected Papers, Martinus Nijhoff, The Hague, 1937).Google Scholar
  7. 7.
    Mehra, J. (1974).Einstein, Hilbert and the Theory of Gravitation. D. Reidel, Dordrecht.Google Scholar
  8. 8.
    Einstein, A. (1915). Zur allgemeinen Relativitätstheorie,Sitzungsber. Preuss. Akad. Wiss.,2, 778 (presented to the Prussian Academy on 4 November 1915).Google Scholar
  9. 9.
    Einstein, A. (1915). Die Feldgleichungen der Gravitation,Sitzungsber. Preuss. Akad. Wiss.,2, 844 (presented to the Prussian Academy on 25 November 1915).Google Scholar
  10. 10.
    Hubert, D. “Die Grundlagen der Physik,Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl., 395 (presented to the Göttingen Academy on November 20, 1915).Google Scholar
  11. 11.
    Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie,Ann. Phys.(Leipzig),49 (4), 769.Google Scholar
  12. 12.
    Lorentz, H. A. (1916) On Einstein's theory of gravitation I, II, III, IV,Versl. K. Akad. Wetench. Amsterdam,24, 1389,24, 1759,25, 268,25, 1380; (1916).Proc. Acad. Amsterdam,19, 1341; (1916).19, 1354; (1916).20, 2; (1916).20, 20 (reprinted in H. A. Lorentz),Collected Papers: see [6],5, 246;5, 260;5, 276;5, (297).Google Scholar
  13. 13.
    Perret, W., and Jeffery, G. B., eds. (1923).The Principle of Relativity (English translation of a collection of original papers on the special and general theory of relativity). Dover, New York.Google Scholar
  14. 14.
    Einstein, A. (1916). Hamiltonsches Prinzip und allgemeine Relativitätstheorie,Sitzungs-ber. Preuss. Akad. Wiss.,2, 1111.Google Scholar
  15. 15.
    Klein, F. (1917). Zu Huberts erster Note über die Grundlagen der Physik,Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl., 469.Google Scholar
  16. 16.
    Klein, F. (1918). Über die Differentialgesetze für die Erhaltung von Impuls und Energie in der Einsteinschen Gravitationstheorie,Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl, 171.Google Scholar
  17. 17.
    Klein, F. Über die Integralform der Erhaltungssätze und die Theorie der Räumlichgeschlossenen Welt,Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl., 394.Google Scholar
  18. 18.
    Levi-Civita, T. (1917). Nozione di parallelismo in una varietà qualunque,Rend. Circ. Mat. Palermo,42, 173.Google Scholar
  19. 19.
    Hessenberg, G. (1917). Vectorielle Begründung der Differentialgeometrie,Math. Ann.,78, 187.Google Scholar
  20. 20.
    Weyl, H.Raum-Zeit-Materie. Springer, Berlin.Google Scholar
  21. 21.
    Weyl, H. (1918). Reine Infinitesimalgeometrie,Math. Z., 2.Google Scholar
  22. 22.
    Weyl, H. (1919).Raum-Zeit-Materie, 3rd ed. Springer, Berlin.Google Scholar
  23. 23.
    Cartan, E. (1922). Sur une généralization de la notion de courbure de Riemann et les espaces à torsion,C. R. Acad. Sci.,174, 593.Google Scholar
  24. 24.
    Cartan, E. (1922). Sur les espaces généralisés et la théorie de la Relativité,C. R. Acad. Sci.,174, 734.Google Scholar
  25. 25.
    Cartan, E. (1922). Sur les equations de structure des espaces généralisés et l'expression analytique du tenseur d'Einstein,C. R. Acad. Sci.,174, 1104.Google Scholar
  26. 26.
    Cartan, E. (1923). Sur les variétés à connexion affine et la théorie de la Relativité généralisée,Ann. ec. Norm.,40, 325; (1924).41, 1; (1925).42, 17.Google Scholar
  27. 27.
    Pauli, W. (1921).Relativitätstheorie, inEnzyklopädie der Mathematischen Wissenschaften, Vol. V19. Teubner, Leipzig.Google Scholar
  28. 28.
    Weyl, H. (1921).Raum-Zeit-Materie, 4th ed. Springer, Berlin.Google Scholar
  29. 29.
    Eddington, A. S. (1921). A generalization of Weyl's theory of electromagnetic and gravitational fields,Proc. R. Soc. London Ser. A99, 104.Google Scholar
  30. 30.
    Eddington, A. S. (1923).The Mathematical Theory of Relativity. Cambridge University Press, Cambridge, England.Google Scholar
  31. 31.
    Eddington, A. S. (1921).Espace, temp et gravitation. Hermann, Paris.Google Scholar
  32. 32.
    Einstein, A. (1923). Zur allgemeinen Relativitätstheorie,Sitzungsber. Pruess. Akad. Wiss., 32.Google Scholar
  33. 33.
    Einstein, A. (1923). Bemerkung zu meiner Arbeit “Zur allgemeinen Relativitätstheorie, ”Sitzungber. Preuss. Akad. Wiss., 76.Google Scholar
  34. 34.
    Einstein, A. (1923). Zur affinen Feldtheorie,Sitzungsber. Preuss. Akad. Wiss., 137.Google Scholar
  35. 35.
    Eddington, A. S. (1924).The Mathematical Theory of Relativity, 2nd ed. (reprint of 1965). Cambridge University Press, Cambridge, England.Google Scholar
  36. 36.
    Einstein, A. (1925). Einheitliche Feldtheorie von Gravitation und Elektrizität,Sitzungber. Pruess. Akad. Wiss., 414.Google Scholar
  37. 37.
    Einstein, A. (1941). Demonstration of the non-existence of gravitational fields with a non-vanishing total mass free of singularities,Rev. Univ. Nacional Tucuman (A),2, 11.Google Scholar
  38. 38.
    Francaviglia, M. (1978). Storia di un lavoro di Albert Eistein,Atti. Ac. Sc. Torino,112, 43.Google Scholar
  39. 39.
    Einstein, A., and Pauli, W. (1943). Non-existence of regular stationary solutions of relativistic field equations,Ann. Math.,44 (2), 131.Google Scholar
  40. 40.
    Einstein, A., and Straus, E. G. (1946). Generalization of the relativistic theory of Gravitation, II,Ann. Math.,47 (2), 731.Google Scholar
  41. 41.
    Einstein, A. (1950).The Meaning of Relativity, 3rd ed. Princeton University Press, Princeton, New Jersey.Google Scholar
  42. 42.
    Einstein, A. (1953).The Meaning of Relativity, 4th ed. Princeton University Press, Princeton, New Jersey.Google Scholar
  43. 43.
    Schrödinger, E. (1947). The relation between metric and affinity,Proc. R. Irish Acad.,51A, 147.Google Scholar
  44. 44.
    Schrödinger, E. (1947). The final affine field laws I, II,Proc. R. Irish Acad.,51A, 163,51A, 205.Google Scholar
  45. 45.
    Weyl, H. (1950).Space-Time-Matter. Dover, New York.Google Scholar
  46. 46.
    Anderson, J. L. (1967).Principles of Relativity Physics. Academic Press, New York.Google Scholar
  47. 47.
    Pauli, W. (1958).Theory of Relativity. Pergamon Press, Oxford (English translation of [27]).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • M. Ferraris
    • 1
  • M. Francaviglia
    • 1
  • C. Reina
    • 2
  1. 1.Istituto di Fisica Matematica dell'UniversitàTorinoItaly
  2. 2.Istituto di Fisica dell'UniversitàMilanoItaly

Personalised recommendations