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Incompressible Einstein–Maxwell fluids with specified electric fields

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Abstract

The Einstein–Maxwell equations describing static charged spheres with uniform density and variable electric field intensity are studied. The special case of constant electric field is also studied. The evolution of the model is governed by a hypergeometric differential equation which has a general solution in terms of special functions. Several classes of exact solutions are identified which may be considered as charged generalizations of the incompressible Schwarzschild interior model. An analysis of the physical features is undertaken for the uniform case. It is demonstrated that uniform density spheres with constant electric field intensity are not realizable with isotropic pressures. This highlights the necessity of studying the criteria for physical admissability of gravitating spheres in general relativity which are solutions to the Einstein–Maxwell equations.

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References

  1. R Tikekar, J. Math. Phys. 31, 2454 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. S D Maharaj and P G L Leach, J. Math. Phys. 37, 430 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. K Komathiraj and S D Maharaj, J. Math. Phys. 48, 042501 (2007)

    Article  MathSciNet  Google Scholar 

  4. R Sharma, S Kamarkar and S Mukherjee, Int. J. Mod. Phys. D 15, 405 (2006)

    Article  ADS  MATH  Google Scholar 

  5. R Sharma and S Mukherjee, Mod. Phys. Lett. A 17, 2535 (2002)

    Article  ADS  Google Scholar 

  6. R Sharma and S Mukherjee, Mod. Phys. Lett. A 16, 1049 (2001)

    Article  ADS  MATH  Google Scholar 

  7. V O Thomas, B S Ratanpaul and P C Vinodkumar, Int. J. Mod. Phys. D 14, 85 (2005)

    Article  ADS  MATH  Google Scholar 

  8. S Thirukkanesh and S D Maharaj, Class. Quantum Grav . 25, 235001 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  9. V Varela, F Rahaman, S Ray, K Chakraborty and M Kalam, Phys. Rev . D 82, 044052 (2010)

    Article  ADS  Google Scholar 

  10. T Feroze and A A Siddiqui, Gen. Relativ . Grav it. 43, 1025 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. P Mafa Takisa and S D Maharaj, Astrophys. Space Sci. 343, 569 (2013)

    Article  ADS  Google Scholar 

  12. S D Maharaj and P Mafa Takisa, Gen. Relativ . Grav it. 44, 1419 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Y K Gupta and S K Maurya, Astrophys. Space Sci. 331, 135 (2011)

    Article  ADS  MATH  Google Scholar 

  14. S K Maurya and Y K Gupta, Astrophys. Space Sci. 333, 149 (2011)

    Article  ADS  MATH  Google Scholar 

  15. T E Kiess, Astrophys. Space Sci. 339, 329 (2012)

    Article  ADS  Google Scholar 

  16. Y K Gupta and M Kumar, Gen. Relativ . Grav it. 37, 575 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. N K Dadhich, A Molina and A Khugaev, Phys. Rev . D 81, 104026 (2010)

    Article  ADS  Google Scholar 

  18. B V Ivanov, Phys. Rev . D 65, 104001 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  19. S Hansraj and S D Maharaj, Int. J. Mod. Phys. D 15, 1311 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  20. M C Durgapal and R Bannerji, Phys. Rev . D 27, 328 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  21. M R Finch and J E F Skea, Class. Quantum Grav . 6, 467 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  22. S Hansraj, Il. Nuov o Cimento 1, 71 (2010)

    MathSciNet  Google Scholar 

  23. M Abramowitz and I A Stegun, Handbook of mathematical functions (Dover, New York, 1965)

    Google Scholar 

  24. S D Maharaj and T Mkhwanazi, Quaestiones Mathematicae 19, 211 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  25. A J John and S D Maharaj, Pramana – J. Phys. 77, 461 (2011)

    Article  ADS  Google Scholar 

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Acknowledgements

SH, SDM and TM thank the National Research Foundation for financial support. SDM acknowledges that this work is based on research supported by the South African Research Initiative of the Department of Science and Technology and the National Research Foundation.

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Authors and Affiliations

  1. Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa

    S HANSRAJ, S D MAHARAJ & T MTHETHWA

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  1. S HANSRAJ
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  2. S D MAHARAJ
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  3. T MTHETHWA
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HANSRAJ, S., MAHARAJ, S.D. & MTHETHWA, T. Incompressible Einstein–Maxwell fluids with specified electric fields. Pramana - J Phys 81, 557–567 (2013). https://doi.org/10.1007/s12043-013-0603-7

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  • DOI: https://doi.org/10.1007/s12043-013-0603-7

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