Advertisement

General Relativity and Gravitation

, Volume 25, Issue 12, pp 1305–1317 | Cite as

The limits of Brans-Dicke spacetimes: a coordinate-free approach

  • F. M. Paiva
  • C. Romero
Research Articles

Abstract

We investigate the limit of Brans-Dicke spacetimesω → ∞ applying a coordinate-free technique. We obtain the limits of some known exact solutions. It is shown that these limits may not correspond to similar solutions in the general relativity theory.

Keywords

Exact Solution General Relativity Differential Geometry Similar Solution 
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.
    Åman, J. E. (1987). “Manual for CLASSI — Classification Programs for Geometries in General Relativity (3rd Provisional Ed.)” University of Stockholm Report.Google Scholar
  2. 2.
    Brans, C. and Dicke, R. H. (1961).Phys. Rev. 124, 925.Google Scholar
  3. 3.
    Cartan, E. (1951),Leçons sur la, Géométrie des Espaces de Riemann (Gauthier-Villars, Paris).Google Scholar
  4. 4.
    Frick, I. (1977). “SHEEP—user's guide.” University of Stockholm Report 77-15.Google Scholar
  5. 5.
    Geroch, R. (1969).Commun. Math. Phys. 13, 180.Google Scholar
  6. 6.
    Hall, G. S. (1985). InProc. 1st Hungarian Relativity Workshop (Balatonszéplak, Hungary).Google Scholar
  7. 7.
    Joly, G. C., and MacCallum, M. A. H. (1990).Class. Quant. Grav. 7, 541.Google Scholar
  8. 8.
    Karlhede, A. (1980).Gen. Rel. Grav. 12, 693.Google Scholar
  9. 9.
    Karlhede, A., and Lindström, U. (1983).Gen. Rel. Grav. 15, 597.Google Scholar
  10. 10.
    Koutras, A. (1992).Class. Quant. Grav. 9, L143.Google Scholar
  11. 11.
    Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).Google Scholar
  12. 12.
    Lorenz, D. (1983). InSolutions of Einstein's Equations: Techniques and Results (Lectures Notes in Physics 205, Springer-Verlag, Berlin).Google Scholar
  13. 13.
    MacCallum, M. A. H., and Åman, J. E. (1986).Class. Quant. Grav. 3, 1133.Google Scholar
  14. 14.
    MacCallum, M. A. H., and Skea, J. E. F. (1993). InAlgebraic Computing in General Relativity: Lecture Notes from the First Brazilian School on Computer Algebra, M. J. Rebouças and W. L. Roque, eds. (Oxford University Press, Oxford), vol. 2.Google Scholar
  15. 15.
    Nariai, H. (1968).Prog. Theor. Phys. 40, 49.Google Scholar
  16. 16.
    Nariai, H. (1969).Prog. Theor. Phys. 42, 544.Google Scholar
  17. 17.
    O'Hanlon, J., and Tupper, B. O. J. (1972).Nuovo Cimento B7, 305.Google Scholar
  18. 18.
    Paiva, F. M., Rebouças, M. J., and MacCallum, M. A. H. (1993).Class. Quant. Grav. 10, 1165.Google Scholar
  19. 19.
    Penrose, R. (1960).Ann. Phys. (NY) 10, 171.Google Scholar
  20. 20.
    Penrose, R. (1972). InGravitation: Problems, Prospects (Dedicated to the memory of A. Z. Petrov) (Izdat, Naukova Dumka, Kiev).Google Scholar
  21. 21.
    Romero, C., and Barros, A. (1993).Phys. Lett. 173A, 243.Google Scholar
  22. 22.
    Romero, C., and Barros, A. (1993).Gen. Rel. Grav. 25, 491.Google Scholar
  23. 23.
    Sánchez, A. R. G., Plebański, J. F., and Przanowski, M. (1991).J. Math. Phys. 32, 2838.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • F. M. Paiva
    • 1
  • C. Romero
    • 2
  1. 1.Centro Brasileiro de Pesquisas FísicasRio de Janeiro - RJBrazil
  2. 2.CP 5008 Departamento de FísicaUniversidade Federal da ParaíbaJoão Pessoa - PBBrazil

Personalised recommendations