New charged shear-free relativistic models with heat flux

Regular Article - Theoretical Physics

Abstract

We study shear-free spherically symmetric relativistic gravitating fluids with heat flow and electric charge. The solution to the Einstein–Maxwell system is governed by the generalised pressure isotropy condition which contains a contribution from the electric field. This condition is a highly nonlinear partial differential equation. We analyse this master equation using Lie’s group theoretic approach. The Lie symmetry generators that leave the equation invariant are found. The first generator is independent of the electromagnetic field. The second generator depends critically on the form of the charge, which is determined explicitly in general. We provide exact solutions to the gravitational potentials using the symmetries admitted by the equation. Our new exact solutions contain earlier results without charge. We show that other charged solutions, related to the Lie symmetries, may be generated using the algorithm of Deng. This leads to new classes of charged Deng models which are generalisations of conformally flat metrics.

Keywords

Master Equation Gravitational Potential Gravitational Collapse Order Differential Equation Stellar Model 

Notes

Acknowledgements

YN, KSG and SDM wish to thank the National Research Foundation and the University of KwaZulu-Natal for support. SDM acknowledges that this work is based on research supported by the South African Research Chair Initiative of the Department of Science and Technology and the National Research Foundation.

References

  1. 1.
    A. Krasinski, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, 1997) CrossRefMATHGoogle Scholar
  2. 2.
    N.O. Santos, Mon. Not. R. Astron. Soc. 216, 403 (1985) ADSGoogle Scholar
  3. 3.
    S.M. Wagh, M. Govender, K.S. Govinder, S.D. Maharaj, P.S. Muktibodh, M. Moodley, Class. Quantum Gravity 18, 2147 (2001) MathSciNetADSCrossRefMATHGoogle Scholar
  4. 4.
    S.D. Maharaj, M. Govender, Int. J. Mod. Phys. D 14, 667 (2005) MathSciNetADSCrossRefMATHGoogle Scholar
  5. 5.
    S.S. Misthry, S.D. Maharaj, P.G.L. Leach, Math. Methods Appl. Sci. 31, 363 (2008) MathSciNetADSCrossRefMATHGoogle Scholar
  6. 6.
    L. Herrera, A. di Prisco, L. Ospino, Phys. Rev. D 74, 044001 (2006) ADSCrossRefGoogle Scholar
  7. 7.
    S. Thirukkanesh, S.S. Rajah, S.D. Maharaj, J. Math. Phys. 53, 032506 (2012) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    O. Bergmann, Phys. Lett. A 82, 383 (1981) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    S.R. Maiti, Phys. Rev. D 25, 2518 (1982) MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    B. Modak, J. Astrophys. Astron. 5, 317 (1984) ADSCrossRefGoogle Scholar
  11. 11.
    A.K. Sanyal, D. Ray, J. Math. Phys. 25, 1975 (1984) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Y. Deng, Gen. Relativ. Gravit. 21, 503 (1989) ADSCrossRefGoogle Scholar
  13. 13.
    A.M. Msomi, K.S. Govinder, S.D. Maharaj, Gen. Relativ. Gravit. 43, 1685 (2011) MathSciNetADSCrossRefMATHGoogle Scholar
  14. 14.
    A.M. Msomi, K.S. Govinder, S.D. Maharaj, Int. J. Theor. Phys. 51, 1290 (2012) MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    B.V. Ivanov, Gen. Relativ. Gravit. 44, 1835 (2012) ADSCrossRefMATHGoogle Scholar
  16. 16.
    K. Komathiraj, S.D. Maharaj, J. Math. Phys. 48, 042501 (2007) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    M.K. Mak, T. Harko, Int. J. Mod. Phys. D 13, 149 (2004) ADSCrossRefMATHGoogle Scholar
  18. 18.
    K. Komathiraj, S.D. Maharaj, Int. J. Mod. Phys. D 16, 1803 (2007) MathSciNetADSCrossRefMATHGoogle Scholar
  19. 19.
    F.S.N. Lobo, Class. Quantum Gravity 23, 1525 (2006) MathSciNetADSCrossRefMATHGoogle Scholar
  20. 20.
    S.D. Maharaj, S. Thirukkanesh, Pramana J. Phys. 72, 481 (2009) ADSCrossRefGoogle Scholar
  21. 21.
    R. Sharma, S.D. Maharaj, Mon. Not. R. Astron. Soc. 375, 1265 (2007) ADSCrossRefGoogle Scholar
  22. 22.
    S. Thirukkanesh, S.D. Maharaj, Math. Methods Appl. Sci. 32, 684 (2009) MathSciNetADSCrossRefMATHGoogle Scholar
  23. 23.
    R. Chan, Int. J. Mod. Phys. D 12, 1131 (2003) ADSCrossRefMATHGoogle Scholar
  24. 24.
    R. Chan, Astron. Astrophys. 368, 325 (2001) ADSCrossRefGoogle Scholar
  25. 25.
    G. Pinheiro, R. Chan, Gen. Relativ. Gravit. 45, 243 (2013) MathSciNetADSCrossRefMATHGoogle Scholar
  26. 26.
    M.C. Kweyama, S.D. Maharaj, K.S. Govinder, Nonlinear Anal., Real World Appl. 13, 1721 (2012) MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    K.S. Govinder, P.G.L. Leach, S.D. Maharaj, Int. J. Theor. Phys. 34, 625 (1995) MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    M.C. Kweyama, K.S. Govinder, S.D. Maharaj, Class. Quantum Gravity 28, 105005 (2011) MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    M.C. Kweyama, K.S. Govinder, S.D. Maharaj, J. Math. Phys. 53, 033707 (2012) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    P.G.L. Leach, S.D. Maharaj, J. Math. Phys. 33, 2023 (1992) MathSciNetADSCrossRefMATHGoogle Scholar
  31. 31.
    A.M. Msomi, K.S. Govinder, S.D. Maharaj, J. Phys. A, Math. Gen. 43, 285203 (2010) MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    S. Dimas, D. Tsoubelis, in Proceedings of the 10th International Conference in Modern Group Analysis, University of Cyprus, Larnaca (2005) Google Scholar
  33. 33.
    G.W. Bluman, S.C. Anco, Symmetry and Integration Methods for Differential Equations (Springer, New York, 2002) MATHGoogle Scholar
  34. 34.
    G.W. Bluman, S. Kumei, Symmetries and Differential Equations (Springer, New York, 1989) CrossRefMATHGoogle Scholar
  35. 35.
    B.J. Cantwell, Introduction to Symmetry Analysis (Cambridge University Press, Cambridge, 2002) MATHGoogle Scholar
  36. 36.
    P. Olver, Equivalence, Invariants and Symmetry (Cambridge University Press, Cambridge, 1995) CrossRefMATHGoogle Scholar
  37. 37.
    P. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 1986) CrossRefMATHGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa

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