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Initial singularity and pure geometric field theories

  • M. I. WanasEmail author
  • Mona M. Kamal
  • Tahia F. Dabash
Regular Article
  • 49 Downloads

Abstract.

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

References

  1. 1.
    S. Hawking, G. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, 1973)Google Scholar
  2. 2.
    A.K. Raychaudhuri, Phys. Rev. 98, 1123 (1955)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    R. Penrose, Phys. Rev. Lett. 14, 57 (1965)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    S. Hawking, R. Penrose, Proc. R. Soc. London A 314, 529 (1970)ADSCrossRefGoogle Scholar
  5. 5.
    M.I. Wanas, Astrophys. Space Sci. 258, 237 (1998)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    M.I. Wanas, Turk. J. Phys. 24, 473 (2000)Google Scholar
  7. 7.
    M.I. Wanas, M.A. Bakry, Int. J. Mod. Phys. A 24, 5025 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    F.I. Mikhail, Ain Shams Univ. Bull. 6, 87 (1962)Google Scholar
  9. 9.
    M.I. Wanas, Adv. High Energy Phys. 2012, 752613 (2012)CrossRefGoogle Scholar
  10. 10.
    M.I. Wanas, N.L. Youssef, W.S. El-Hanafy, S.N. Osman, Adv. Math. Phys. 2016, 1037849 (2016)CrossRefGoogle Scholar
  11. 11.
    M.I. Wanas, A generalized field theory and its applications in cosmology, PhD Thesis, Cairo University (1975)Google Scholar
  12. 12.
    H.P. Robertson, Ann. Math. 33, 496 (1932)MathSciNetCrossRefGoogle Scholar
  13. 13.
    F.I. Mikhail, M.I. Wanas, Proc. R. Soc. London A 356, 471 (1977)ADSCrossRefGoogle Scholar
  14. 14.
    M.I. Wanas, Mona M. Kamal, Adv. High Energy Phys. 2014, 687103 (2014)CrossRefGoogle Scholar
  15. 15.
    M.I. Wanas, N.L. Youssef, A.M. Sid-Ahmed, Class. Quantum Grav. 27, 045005 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    M.I. Wanas, S.N. Osman, R.I. El-Kholy, Open Phys. 13, 247 (2015)CrossRefGoogle Scholar
  17. 17.
    M.I. Wanas, N.L. Youssef, W.S. El-Hanafy, Gravit. Cosmol. 23, 105 (2017)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    P. Luz, V. Vitagliano, Phys. Rev. D 96, 024021 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    F.D. Albareti, J.A.R. Cembranos, J.A.R. Cembranos, JCAP 2012, 20 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    L. Fabbri, Non-Singular Spinors in Gravity with Propagating Torsion, arXiv:1702.03864 (2017)Google Scholar
  21. 21.
    F.I. Mikhail, M.I. Wanas, A.M. Eid, Astrophys. Space Sci. 228, 221 (1995)ADSCrossRefGoogle Scholar
  22. 22.
    M.I. Wanas, M.E. Kahil, Gen. Relativ. Gravit. 31, 1921 (1999)ADSCrossRefGoogle Scholar
  23. 23.
    M.I. Wanas, M. Melek, M.E. Kahil, Gravit. Cosmol. 6, 319 (2000)ADSGoogle Scholar
  24. 24.
    M.I. Wanas, Int. J. Geom. Methods Mod. Phys. 4, 373 (2007)MathSciNetCrossRefGoogle Scholar
  25. 25.
    M.I. Wanas, Samah A. Ammar, Cent. Eur. J. Phys. 11, 936 (2013)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • M. I. Wanas
    • 1
    Email author
  • Mona M. Kamal
    • 2
  • Tahia F. Dabash
    • 3
  1. 1.Astronomy Department, Faculty of ScienceCairo UniversityGizaEgypt
  2. 2.Mathematics Department, Faculty of GirlsAin Shams UniversityCairoEgypt
  3. 3.Mathematics Department, Faculty of ScienceTanta UniversityTantaEgypt

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