Advertisement

Lemaître-Tolman-Bondi model: Solutions of the cosmological equation

  • Antonio Zecca
Regular Article
  • 177 Downloads

Abstract

The solution of the generalized Newton-like equation of the Lemaître-Tolman-Bondi cosmological model with cosmological constant (\( \Lambda\) LTB) is reconsidered. Parametric solutions, obtained by different methods, are further elaborated by means of the properties of the Weierstrass elliptic functions. This allows significant new aspects of the solutions to be emphasized. Also factorized parametric solutions are determined by applying an integration method previously considered. The scalar, Dirac and spin 1 field equations become separable in the space-time given by the factorized parametric solutions.

Keywords

Dark Energy Cosmological Constant Cosmological Model Parametric Form Parametric 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.

References

  1. 1.
    G. Lemaitre, Gen. Relativ. Gravit. 29, 641 (1997)ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    R.C. Tolman, Gen. Relativ. Gravit. 29, 935 (1997)ADSCrossRefGoogle Scholar
  3. 3.
    H. Bondi, Mon. Not. R. Astron. Soc. 107, 410 (1947)ADSMATHMathSciNetGoogle Scholar
  4. 4.
    A. Krasinski, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, 1997)Google Scholar
  5. 5.
    A.E. Romano, P. Chen, JCAP 10, 016 (2011)CrossRefGoogle Scholar
  6. 6.
    M.-N. Celerier, K. Bolejko, A. Krasinski, Astron. Astrophys. 518, A21 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    A. Zecca, Gen. Relativ. Gravit. 32, 1197 (2000)ADSCrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    A. Zecca, Nuovo Cimento B 116, 341 (2001)ADSMathSciNetGoogle Scholar
  9. 9.
    A. Zecca, in Aspects of today Cosmology, edited by Antonio Alfonso-Faus (Intech, 2011)Google Scholar
  10. 10.
    A. Zecca, Separation of spin 0, 1/2, 1 field equations in Lemaitre-Tolman-Bondi cosmological model with cosmological constant, to be published in Int. J. Theor. Phys., DOI:10.1007/s10773-013-1795-9
  11. 11.
    A. Zecca, Nuovo Cimento B 106, 413 (1991)ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    A. Zecca, Nuovo Cimento B 116, 1195 (2001)ADSMathSciNetGoogle Scholar
  13. 13.
    M. Demianski, J.P. Lasota, Nat. Phys. Sci. 241, 53 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    W. Abramovitz, I.E. Stegun, Handbook of Mathematical Functions (Dover Publication, New York, 1960)Google Scholar
  15. 15.
    I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series and product (Academic Press, New York, 1965)Google Scholar
  16. 16.
    A. Zecca, Int. J. Theor. Phys. 39, 377 (2000)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    R. Illge, Commun. Math. Phys. 158, 433 (1993)ADSCrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    A. Zecca, Int. J. Theor. Phys. 51, 438 (2012)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Antonio Zecca
    • 1
  1. 1.Dipartimento di Fisica dell’Università degli Studi di MilanoMilanoItaly

Personalised recommendations