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General Relativity and Gravitation

, Volume 44, Issue 2, pp 367–389 | Cite as

Intrinsic vanishing of energy and momenta in a universe

  • Ramon Lapiedra
  • Juan Antonio Morales-Lladosa
Research Article

Abstract

We present a new approach to the question of properly defining energy and momenta for non asymptotically Minkowskian spaces in General Relativity, in the case where these energy and momenta are conserved. In order to do this, we first prove that there always exist some special Gauss coordinates for which the conserved linear and angular 3-momenta intrinsically vanish. This allows us to consider the case of creatable universes (the universes whose proper 4-momenta vanish) in a consistent way, which is the main interest of the paper. When applied to the Friedmann-Lemaître-Robertson-Walker case, perturbed or not, our formalism leads to previous results, according to most literature on the subject. Some future work that should be done is mentioned.

Keywords

Energy and momenta of the Universe Non asymptotic flatness Intrinsic vanishing of momenta 

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References

  1. 1.
    Szabados, L.B.: Living Rev. Relativ. 12, 4. Update of lrr-2004-4 (2009)Google Scholar
  2. 2.
    Katz J., Bic̆ák J., Lynden-Bell D.: Phys. Rev. D 55, 5957 (1997) See also gr-qc/0504041 for some corrected misprintsMathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Nester J.M.: Class. Quantum Grav. 21, S261–S280 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    Brown J.D., York J.W. Jr: Phys. Rev. D 47, 1407 (1993)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Hawking S.W., Horowitz G.: Class. Quantum Grav. 13, 1487 (1996)MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Silva S.: Nucl. Phys. B 558, 391 (1999)ADSMATHCrossRefGoogle Scholar
  7. 7.
    Fatibene L., Ferraris M., Francaviglia M.: Int. J. Geom. Methods Mod. Phys. 2, 373 (2005)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Bibbona E., Fatibene L., Francaviglia M.: Int. J. Geom. Methods Mod. Phys. 6, 1193 (2009)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Hayward S.A.: Phys. Rev. D 49, 831 (1994)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Cooperstook F.I.: Gen. Relativ. Gravit. 26, 323 (1994)ADSCrossRefGoogle Scholar
  11. 11.
    Chang C-C., Nester J.M., Chen C-M.: Phys. Rev. Lett. 83, 1897 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    Vargas T.: Gen. Relativ. Gravit. 36, 1255 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Chen C.-M., Liu J.-L., Nester J.M.: Mod. Phys. Lett. A. 22, 2039 (2007)ADSMATHCrossRefGoogle Scholar
  14. 14.
    Carini M., Fatibene L., Francaviglia M.: Int. J. Geom. Methods Mod. Phys. 4, 907 (2007)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Ferrando J.J., Lapiedra R., Morales J.A.: Phys. Rev. D 75, 124003 (2007)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Weinberg S.: Gravitation and Cosmology, Chapter 5, epigraph 6. Wiley, London (1972)Google Scholar
  17. 17.
    Murchadha N.Ó.: J. Math. Phys. 27, 2111 (1986)MathSciNetADSMATHCrossRefGoogle Scholar
  18. 18.
    Alcubierre M.: Introduction to 3 + 1 Numerical Relativity. Oxford University Press, Oxford (2008)MATHCrossRefGoogle Scholar
  19. 19.
    Banerjee N., Sen S.: Pramana J. Phys. 49, 609 (1997)ADSCrossRefGoogle Scholar
  20. 20.
    Xulu S.S.: Int. J. Theor. Phys. 39, 1153 (2000)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Nester J.M., So L.L., Vargas T.: Phys. Rev. D 78, 044035 (2008)MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Pitts J.B.: Gen. Relativ. Gravit. 42, 601 (2010)MathSciNetADSMATHCrossRefGoogle Scholar
  23. 23.
    Albrow M.G.: Nature 241, 56 (1973)ADSGoogle Scholar
  24. 24.
    Tryon E.P.: Nature 246, 396 (1973)ADSCrossRefGoogle Scholar
  25. 25.
    Lapiedra R., Sáez D.: Phys. Rev. D 77, 104011 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    Lapiedra R., Morales-Lladosa J.A.: J. Phys. Conf. Ser. 229, 012053 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    Landau L., Lifchitz E.M.: The Classical Theory of Fields. Pergamon Press, New York (1962)MATHGoogle Scholar
  28. 28.
    Poisson E.: A Relativistic Toolkit, The Mathematics of Black Hole Mechanics. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  29. 29.
    Rosen N.: Gen. Relativ. Gravit. 26, 319 (1994)ADSCrossRefGoogle Scholar
  30. 30.
    Garecki J.: Gen. Relativ. Gravit. 27, 55 (1995)MathSciNetADSMATHCrossRefGoogle Scholar
  31. 31.
    Garecki J.: Acta Phys. Pol. 39, 781 (2008)MathSciNetADSGoogle Scholar
  32. 32.
    Mitra A.: Gen. Relativ. Gravit. 42, 443 (2010)ADSMATHCrossRefGoogle Scholar
  33. 33.
    Berman S.A.: Int. J. Theor. Phys. 48, 3278 (2009)MATHCrossRefGoogle Scholar
  34. 34.
    Afshar M.M.: Class. Quantum Grav. 26, 225005 (2009)MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    Faraoni V., Cooperstock F.I.: Astrophys. J. 587, 483 (2003)ADSCrossRefGoogle Scholar
  36. 36.
    Lachièze-Rey M., Luminet J.P.: Phys. Rep. 254, 135 (1995)MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    Jaffe T.R., Banday A.J, Eriksen H.K., Górski K.M., Hansen F.K.: Astrophys. J. 629, L1 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Departament d’Astronomia i AstrofísicaUniversitat de ValènciaBurjassotSpain

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