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Invariant Solutions of Inhomogeneous Universe with Electromagnetic Field in Lyra Geometry

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Abstract

The present study deals with the cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electro-magnetic field in Lyra geometry. Lie group analysis has been used to identify the generators (symmetries) that leave the given system of partial differential equations (field equations) invariant. With the help of canonical variables associated with these generators, the assigned system of partial differential equations is reduced to an ordinary differential equations whose simple solutions provide nontrivial solutions of the original system. They obtained a new class of invariant (similarity) solutions by considering the potentials of metric and displacement field are functions of coordinates t and x. The physical behavior of the derived models are also discussed.

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References

  1. Kaloper, N., et al.: Nucl. Phys. B 452, 677 (1995)

    Article  ADS  Google Scholar 

  2. Livio, M.: The accelerating universe. Wiley (2000)

  3. Weinberg, S.: Gravitation and cosmology. Wiley (1972)

  4. Ya, B., Zeldovich, A., Ruzmainkin, A., Sokoloff, D.D.: Magnetic Field in Astrophysics. (Gordon and Breach, New Yark) (1993)

  5. Horrison, E.R.: Rev. Phys. Lett 30, 188 (1973)

    Article  Google Scholar 

  6. Melvin, M.A.: Acad. Ann. NY Sci 262, 253 (1975)

  7. Barrow, J.D.: Rev, Phys. D 55, 7451 (1997)

    Google Scholar 

  8. Asseo, E., Sol, H.: Phys. Rep. 6, 148 (1987)

    Google Scholar 

  9. Melvin, M.A.: Vol. 253, p 262

  10. Pudritz, R., Silk, J.: Astrophys. J. 342, 650 (1989)

    Article  ADS  Google Scholar 

  11. Kim, K.T., Tribble, P.G., Kronberg, P.P.: Astrophys. J. 379, 80 (1991)

    Article  ADS  Google Scholar 

  12. Perley, R., Taylor, G.: Astrophys. J. 101, 1623 (1991)

    ADS  Google Scholar 

  13. Kronberg, P.P., Perry, J.J., Zukowski, E.L.: Astrophys. J. 387, 528 (1991)

    Article  ADS  Google Scholar 

  14. Wolfe, A.M., Lanzetta, K., Oren, A.L.: Astrophys. J. 388, 17 (1992)

    Article  ADS  Google Scholar 

  15. Kulsrud, R., Cen, R., Ostriker, J.P., Ryu, D.: Astrophys. J. 380, 481 (1997)

    Article  ADS  Google Scholar 

  16. Zweibel, E.G., Heiles, C.: Nature 385, 131 (1997)

    Article  ADS  Google Scholar 

  17. Sengupta, S., et al.: JCAP 0312, 001 (2003)

    Article  Google Scholar 

  18. Lyra, G.: Math, Z. 54, 52 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  19. Sen, D.K.: Phys. Z. 149, 311 (1957)

    Article  MATH  ADS  Google Scholar 

  20. Senand, D.K., Dunn, K.A.: J Math. Phys. 12, 578 (1971)

    Article  ADS  Google Scholar 

  21. Ali, A.T., Hassan, E.R.: Appl. Math. Comp. 217(2), 451 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. El-Sabbagh, M.F., Ali, A.T.: Commun. Nonlinear Sci. Numer. Simulat. 6(2), 151 (2005)

    MathSciNet  Google Scholar 

  23. El-Sabbagh, MF, Ali, AT.: Commun. Nonlinear Sci. Numer. Simulat. 13, 1758 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  24. Ovsiannikov, L.V.: Group analysis of differential equations. Translated by Chapovsky, Y. Ed. Ames W.F.Academic Press, New York-London (1982)

    Google Scholar 

  25. Ibragimov, N.H.: Transformation groups applied to mathematical physics:, D. Reidel, Dortrecht (1985)

  26. Ali, A.T.: J. Comp. Appl. Math 235, 4117 (2011)

    Article  MATH  Google Scholar 

  27. AT, Ali.: Phys. Scr. 79(3), 035006 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  28. Attallah, S.K., El-Sabbagh, M.F., Ali, A.T.: Commun Nonlinear Sci Numer Simulat 12(7), 1153 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  29. Mekheimer, K.S., Husseny, S.Z., Ali A.T., Abo-Elkhair, R.E.: Phys. Scr. 83(1), 015017 (2011)

    Article  ADS  Google Scholar 

  30. Bluman, G.W., Kumei, S.: Symmetries and differential equations in applied sciences, New York (1989)

  31. Olver, P.J.: Application of lie groups to differential equations in graduate texts in mathematics, Vol. 107. Second edition, Springer, New York (1993)

    Book  Google Scholar 

  32. Stephani, H.: Differential equations: their solutions using symmetries. Cambridge University Press (1989)

  33. Lichnerowicz, A.: Relativistic hydrodynamics and magneto-hydro-dynamics, 93 (1967)

  34. Synge, J.L.: Relativity: the general theory, p 356. North-Holland Publ, Amsterdam (1960)

    MATH  Google Scholar 

  35. Pradhan, A., Mathur, P.: Fizika B. 18, 243 (2009)

    Google Scholar 

  36. Raychaudhuri, A.K.: Theoritical cosmology. Oxford, p 80 (1979)

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Acknowledgments

FR would like to thank the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India, for research facility. FR is also grateful to UGC, India, for financial support under its Research Award Scheme. AM is thankful to DST for providing financial support under INSPIRE programme. We are thankful to the referee for his valuable suggestions.

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Authors and Affiliations

  1. King Abdulaziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah, 21589, Saudi Arabia

    Ahmad T Ali

  2. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt

    Ahmad T Ali

  3. Department of Mathematics, Jadavpur University, Kolkata, 700 032, West Bengal, India

    F Rahaman & A Mallick

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  1. Ahmad T Ali
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  2. F Rahaman
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  3. A Mallick
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Correspondence to F Rahaman.

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Ali, A.T., Rahaman, F. & Mallick, A. Invariant Solutions of Inhomogeneous Universe with Electromagnetic Field in Lyra Geometry. Int J Theor Phys 53, 4197–4210 (2014). https://doi.org/10.1007/s10773-014-2171-0

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  • DOI: https://doi.org/10.1007/s10773-014-2171-0

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