Advertisement

General Relativity and Gravitation

, Volume 15, Issue 11, pp 1051–1066 | Cite as

The cosmological principle and a generalization of Newton's theory of gravitation

  • Folkert Müller-Hoissen
Research Articles

Abstract

Using the notion of Galilei manifolds a geometric formulation of the cosmological principle for the prerelativistic theory of gravitation is presented. This is applied to a generalization of the Newton-Cartan theory which admits solutions with a curved Galilei structure. Furthermore, the limit relation between this theory and some relativistic theories is discussed.

Keywords

Field Equation Curvature Tensor Limit Relation Friedmann Equation Newtonian Theory 
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.
    Cartan, É. (1923).Ann. Sci. Ecole Norm. Sup.,40, 325.MATHMathSciNetGoogle Scholar
  2. 2.
    Cartan, É. (1924).Ann. Sci. Ecole Norm. Sup.,41, 1.MATHMathSciNetGoogle Scholar
  3. 3.
    Trautman, A. (1963).C. R. Acad. Sci. Paris,257, 617.MATHMathSciNetGoogle Scholar
  4. 4.
    Trautman, A. (1966).In Perspectives in Geometry and Relativity, Hoffmann, B., ed. (Indiana Univ. Press, Bloomington and London), p. 413.Google Scholar
  5. 5.
    Dombrowski, H. D., and Horneffer, K. (1964).Nachr. Akad. Wiss. Göttingen, Math.-phys. Klasse, 233.Google Scholar
  6. 6.
    Dombrowski, H. D., and Horneffer, K. (1964).Math. Zeitschr.,86, 291.MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Horneffer, K. (1966).Arch. Rat. Mech. Anal.,23, 239.MATHMathSciNetGoogle Scholar
  8. 8.
    Künzle, H. P. (1972).Ann. Inst. Henri Poincaré,17, 337.Google Scholar
  9. 9.
    Ehlers, J. (1981). InGrundlagenprobleme der modernen Physik, Nitsch, J., et al., eds. (Bibliographisches Institut, Mannheim), p. 65.Google Scholar
  10. 10.
    Toupin, R. A. (1957/58).Arch. Rat. Mech. Anal.,1, 181.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Havas, P. (1964).Rev. Mod. Phys.,36, 938.MATHMathSciNetCrossRefADSGoogle Scholar
  12. 12.
    Dixon, W. G. (1975).Commun. Math. Phys.,45, 167.MATHMathSciNetCrossRefADSGoogle Scholar
  13. 13.
    Duval, C., and Künzle, H. P. (1977).C. R. Acad. Sci. Paris,285A, 813.Google Scholar
  14. 14.
    Duval, C., and Künzle, H. P. (1978).Rep. Math. Phys.,13, 351.MATHMathSciNetCrossRefADSGoogle Scholar
  15. 15.
    Lawitzky, G. (1980).Gen. Rel. Grav.,12, 903.MATHMathSciNetCrossRefADSGoogle Scholar
  16. 16.
    Kuchař, K. (1980).Phys. Rev. D,22, 1285.MathSciNetCrossRefADSGoogle Scholar
  17. 17.
    Trümper, M. (1983).Ann. Phys.,149, 203.MATHCrossRefADSGoogle Scholar
  18. 18.
    Goenner, H. (1982).Phys. Lett.,93A, 469.MathSciNetADSGoogle Scholar
  19. 19.
    Burdet, G., Duval, C., and Perrin, M. (1983). Cartan structures on Galilean manifolds: the chronoprojective geometry,J. Math. Phys. (to appear).Google Scholar
  20. 20.
    Friedrichs, K. (1927).Math. Ann.,98, 566.MATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Dautcourt. G. (1964).Acta Phys. Pol.,25, 637.MathSciNetGoogle Scholar
  22. 22.
    Künzle, H. P. (1976).Gen. Rel. Grav.,7, 445.MATHADSGoogle Scholar
  23. 23.
    Hehl, F., Nitsch, J., and von der Heyde, P. (1980). InGeneral Relativity and Gravitation, Vol. 1, Held, A., ed. (Plenum Press, New York), p. 329.Google Scholar
  24. 24.
    Hayashi, K., and Shirafuji, T. (1980).Progr. Theor. Phys.,64, 866, 883, 1435, 2222.MATHMathSciNetADSGoogle Scholar
  25. 25.
    Heckmann, O., and Schücking, E. (1955).Z. Astrophys.,38, 95.MATHMathSciNetADSGoogle Scholar
  26. 26.
    Heckmann, O., and Schücking, E. (1959). InHandbuch der Physik, Flügge, S., ed. (Springer, Berlin), vol. 53, p. 489.Google Scholar
  27. 27.
    Ehlers, J., and Rienstra, W. (1969).Astrophys. J.,155, 105.CrossRefADSGoogle Scholar
  28. 28.
    Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry, Vol. 1 (Interscience Publishers, John Wiley and Sons, New York).MATHGoogle Scholar
  29. 29.
    Müller-Hoissen, F. (1982). A gauge theoretical approach to space-time structures,Ann. Inst. Henri Poincaré (to appear).Google Scholar
  30. 30.
    Ellis, G. F. R. (1971). InGeneral Relativity and Cosmology, Sachs, B. K., ed. (Academic Press, New York), p. 104.Google Scholar
  31. 31.
    Souriau, J.-M. (1975).Colloques Int. C.N.R.S.,237, 59.Google Scholar
  32. 32.
    Müller-Hoissen, F. (1982).Phys. Lett.,92A, 433.ADSGoogle Scholar
  33. 33.
    McCrea, W., and Milne, E. (1934).Quart. J. Math., Oxford Ser.,5, 73.MATHGoogle Scholar
  34. 34.
    Fairchild, E. E., Jr. (1977).Phys. Rev. D,16, 2438.MathSciNetCrossRefADSGoogle Scholar
  35. 35.
    Keres, H. (1964).Sov. Phys. JETP,19, 1174.MathSciNetGoogle Scholar
  36. 36.
    Koppel, A. (1974).Izv. Akad. Nauk Est. SSR Fiz. Mat.,23, 370.MATHMathSciNetGoogle Scholar
  37. 37.
    Koppel, A. (1975).Izv. Akad. Nauk Est. SSR Fiz. Mat.,24, 297.MathSciNetGoogle Scholar
  38. 38.
    Koppel, A. (1975).Sov. Phys. J.,18, 1232.CrossRefGoogle Scholar
  39. 39.
    Koppel, A. (1980).Tartu Riikliku Ülikooli Toimetised, Acta et commentations Universitatis Tartuensis, No. 520.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Folkert Müller-Hoissen
    • 1
  1. 1.Institute for Theoretical PhysicsGöttingenFederal Republic of Germany

Personalised recommendations