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Exact solutions of Einstein field equations in perfect fluid distribution using Lie symmetry method

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Abstract

The exact non-static accelerating solutions of Einstein field equations in perfect fluid distribution with nonzero shear in the texture gas dominated universe corresponding to an indefinite non-degenerate metric in cartesian coordinates are obtained in a gravitational field of Petrov type D. Lie symmetry method is used for reduction and finding trigonometric solutions. By following multiplier approach, the conservation laws are obtained. The graphical representations are also shown.

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References

  1. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt, Exact Solutions of Einstein’s Field Equations, 2nd edn. (Cambridge University Press, New York, 2003)

    Book  Google Scholar 

  2. S.P. Puri, General Theory of Relativity (Pearson, Delhi, 2013)

    Google Scholar 

  3. R.G. Vishwakarma, Pramana J. Phys. 85(6), 1101–1110 (2015)

    Article  ADS  Google Scholar 

  4. S. Kumar, Pratibha, Y.K. Gupta, Int. J. Mod. Phys. A 25(20), 3993–4000 (2010)

    Article  ADS  Google Scholar 

  5. M. Kumar, Y.K. Gupta, Pramana J. Phys. 74(6), 883–893 (2010)

    Article  ADS  Google Scholar 

  6. M. Kumar, D. Tanwar, Comput. Math. Appl. 76(11–12), 2535–2548 (2018)

    Article  MathSciNet  Google Scholar 

  7. S. Kumar, Nonlinear Dyn. 87, 1153–1157 (2016)

    Article  Google Scholar 

  8. R. Naz, J. Appl. Math. 2012, 871253 (2012)

    Google Scholar 

  9. B. O’Neill, Semi-Riemannian Geometry (Academic Press Limited, London, 1983)

    MATH  Google Scholar 

  10. A.M. Wazwaz, Math. Comput. Model. 40, 499–508 (2004)

    Article  Google Scholar 

  11. A. Biswas, Nonlinear Dyn. 58, 345–348 (2009)

    Article  Google Scholar 

  12. O. Gron, S. Johannesen, Eur. Phys. J. Plus 126(9), 89 (2011)

    Article  Google Scholar 

  13. A. Chaudhuri, S. Chaudhuri, Eur. Phys. J. Plus 132(11), 472 (2017)

    Article  Google Scholar 

  14. P.J. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 1986)

    Book  Google Scholar 

  15. G.W. Bluman, S.C. Anco, Symmetries and Integration Methods for Differential Equations, vol. 154 (Springer, New York, 2002)

    MATH  Google Scholar 

  16. O. Gron, Eur. Phys. J. Plus 128(8), 92 (2013)

    Article  Google Scholar 

  17. S.C. Anco, G.W. Bluman, Eur. J. Appl. Math. 13(05), 545–566 (2002)

    Article  Google Scholar 

  18. S.C. Anco, G.W. Bluman, Eur. J. Appl. Math. 13(05), 567–585 (2002)

    Article  Google Scholar 

  19. N.H. Ibragimov, J. Math. Anal. Appl. 333, 311–328 (2007)

    Article  MathSciNet  Google Scholar 

  20. R. Naz, I. Naeem, M.D. Khan, Math. Probl. Eng. 2013, 897912 (2013)

    Article  Google Scholar 

  21. A.H. Kara, F.M. Mahomed, J. Nonlinear Math. Phys. 9(2), 60–72 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  22. L. Kaur, R.K. Gupta, Maejo Int. J. Sci. Technol. 7(01), 133–144 (2013)

    Google Scholar 

  23. A. Einstein, N. Rosen, J. Frankl. Inst. 223, 43–54 (1937)

    Article  ADS  Google Scholar 

  24. P.S. Wesson, Astrophys. J. 378, 466–470 (1991)

    Article  ADS  Google Scholar 

  25. J.R. Gott III, M.J. Rees, Mon. Not. R. Astron. Soc. 227, 453–459 (1987)

    Article  ADS  Google Scholar 

  26. E.W. Kolb, Astrophys. J. 344, 543–550 (1989)

    Article  ADS  Google Scholar 

  27. J.P. de Leon, Gen. Relativ. Gravit. 25(11), 1123–1137 (1993)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

First author (Divya Jyoti) is very much thankful to CSIR for providing financial assistance in terms of JRF fellowship via letter with Sr. No. 1061841352 and Ref. No. 17/06/2018(i)EU-V. Rajesh Kumar Gupta and Sachin Kumar thank the National Board of Higher Mathematics for financial support provided through Ref. No. 2/48(16)/2016/NBHM(R.P.)/R&D II/14982.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, 151001, India

    Divya Jyoti, Sachin Kumar & Rajesh Kumar Gupta

  2. Department of Mathematics, Central University of Haryana, Mahendragarh, Haryana, India

    Rajesh Kumar Gupta

Authors
  1. Divya Jyoti
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  2. Sachin Kumar
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  3. Rajesh Kumar Gupta
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Correspondence to Sachin Kumar.

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Jyoti, D., Kumar, S. & Gupta, R.K. Exact solutions of Einstein field equations in perfect fluid distribution using Lie symmetry method. Eur. Phys. J. Plus 135, 604 (2020). https://doi.org/10.1140/epjp/s13360-020-00622-2

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00622-2

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