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Dynamics of charged plane symmetric gravitational collapse

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Abstract

In this paper, we study dynamics of the charged plane symmetric gravitational collapse. For this purpose, we discuss non-adiabatic flow of a viscous fluid and deduce the results for adiabatic case. The Einstein and Maxwell field equations are formulated for general plane symmetric spacetime in the interior. Junction conditions between the interior and exterior regions are derived. For the non-adiabatic case, the exterior is taken as plane symmetric charged Vaidya spacetime while for the adiabatic case, it is described charged plane symmetric spacetime. Using Misner and Sharp formalism, we obtain dynamical equations to investigate the effects of different forces over the rate of collapse. In non-adiabatic case, a dynamical equation is joined with transport equation of heat flux. Finally, a relation between the Weyl tensor and energy density is found.

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References

  1. Penrose R.: Phys. Rev. Lett. 14, 57 (1965)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Oppenheimer J.R., Snyder H.: Phys. Rev. 56, 455 (1939)

    Article  MATH  ADS  Google Scholar 

  3. Markovic D., Shapiro S.L.: Phys. Rev. D61, 084029 (2000)

    ADS  Google Scholar 

  4. Misner C.W., Sharp D.: Phys. Rev. 136, B571 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  5. Darmois, G.: Memorial des Sciences Mathematiques. Gautheir-Villars, Paris, Fasc. 25 (1927)

  6. Lichnerowicz, A.: Theories Relativistes de le Gravitation et de l’ Electro magne’tisme, Masson, Chap I, III (1955)

  7. Brien, S.O., Synge, J.L.: Comm. of the Dublin Institute for Advanced Studies, A9 (1952)

  8. Bonnor W.B., Vickers P.A.: Gen. Relativ. Gravit. 13, 29 (1981)

    ADS  Google Scholar 

  9. Herrera, L., Santos, N.O.: Gen. Relativ. Gravit. gr-qc/0907.2253 (to appear) (2010)

  10. Sharif M., Iqbal K.: Mod. Phys. Lett. A24, 1533 (2009)

    MathSciNet  ADS  Google Scholar 

  11. Sharif, M., Ahmad, Z.: Mod. Phys. Lett. A22, 1493, ibid. 2947 (2007)

  12. Herrera L., Santos N.O., Wang A.: Phys. Rev. D78, 084026 (2008)

    ADS  Google Scholar 

  13. Herrera L., Santos N.O.: Phys. Rev. D70, 084004 (2004)

    MathSciNet  ADS  Google Scholar 

  14. Di Prisco A., Herrera L., MacCallum M.A.H., Santos N.O.: Phys. Rev. D80, 064031 (2009)

    MathSciNet  ADS  Google Scholar 

  15. Nakao K., Morisawa Y.: Class. Quantum Gravit. 21, 2101 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. Sharif M., Rehmat Z.: Gen. Relativ. Gravit. 42, 1795 (2010)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. Sharif M., Ahmad Z.: Int. J. Mod. Phys. A23, 181 (2008)

    MathSciNet  ADS  Google Scholar 

  18. Chakraborty S., Debnath U.: Mod. Phys. Lett. A20, 1451 (2005)

    ADS  Google Scholar 

  19. Chakraborty S., Chakraborty S., Debnath U.: Int. J. Mod. Phys. D16, 833 (2007)

    MathSciNet  ADS  Google Scholar 

  20. Kurita Y., Nakao K.: Phys. Rev. D73, 064022 (2006)

    MathSciNet  ADS  Google Scholar 

  21. Wang A., Wu Y., Wu Z.C.: Gen. Relativ. Gravit. 36, 1225 (2004)

    Article  MATH  ADS  Google Scholar 

  22. Nath S., Debnath U., Chakraborty S.: Astrophys. Space Sci. 313, 431 (2008)

    Article  MATH  ADS  Google Scholar 

  23. Virbhadra K.S., Narasimha D., Chitre S.M.: Astron. Astrophys. 337, 1 (1998)

    ADS  Google Scholar 

  24. Virbhadra K.S., Ellis G.F.R.: Phys. Rev. D62, 084003 (2000)

    MathSciNet  ADS  Google Scholar 

  25. Virbhadra K.S., Ellis G.F.R.: Phys. Rev. D65, 103004 (2002)

    MathSciNet  ADS  Google Scholar 

  26. Claudel C.M., Virbhadra K.S., Ellis G.F.R.: J. Math. Phys. 42, 818 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  27. Virbhadra K.S., Keeton C.R.: Phys. Rev. D77, 124014 (2008)

    ADS  Google Scholar 

  28. Virbhadra K.S.: Phys. Rev. D60, 104041 (1999)

    MathSciNet  ADS  Google Scholar 

  29. Virbhadra K.S.: Phys. Rev. D79, 083004 (2009)

    ADS  Google Scholar 

  30. Sharif M., Abbas G.: Mod. Phys. Lett. A24, 2551 (2009)

    MathSciNet  ADS  Google Scholar 

  31. Sharif M., Abbas G.: J. Korean Phys. Soc. 56, 529 (2010)

    Article  ADS  Google Scholar 

  32. Di Prisco A., Herrera L., Denmat G.L., MacCallum M.A.H., Santos N.O.: Phys. Rev. D76, 064017 (2007)

    ADS  Google Scholar 

  33. Maartens, R.: Causal Thermodynamics in Relativity, astro-ph/9609119

  34. Zannias T.: Phys. Rev. D41, 3252 (1990)

    MathSciNet  ADS  Google Scholar 

  35. Kramer D., Stephani H., MacCallum M.A.H., Herlt E.: Exact Solutions to Einstein Field Equations. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  36. Bekenstein J.: Phys. Rev. D4, 2185 (1971)

    ADS  Google Scholar 

  37. Misner C.: Phys. Rev. 137, B1360 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  38. Penrose R.: In: Hawking, S.W., Israel, W. (eds) General Relativity, An Einstein Centenary Survey, pp. 581–638. Cambridge University Press, Cambridge (1979)

  39. Herrera L., Di Prisco A., Martin J., Ospino J., Santos N.O., Troconis O.: Phys. Rev. D69, 084026 (2004)

    ADS  Google Scholar 

  40. Bonnor W.B.: Phys. Lett. A122, 305 (1987)

    MathSciNet  ADS  Google Scholar 

  41. Goode S.W., Coley A., Wainwright J.: Class. Quantum Gravit. 9, 445 (1992)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  42. Pelavas, N., Lake, K.: gr-qc/9811085

  43. Herrera L.: Int. J. Mod. Phys. D15, 2197 (2006)

    MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, 54590, Pakistan

    M. Sharif & Aisha Siddiqa

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  1. M. Sharif
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  2. Aisha Siddiqa
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Correspondence to M. Sharif.

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Sharif, M., Siddiqa, A. Dynamics of charged plane symmetric gravitational collapse. Gen Relativ Gravit 43, 73–91 (2011). https://doi.org/10.1007/s10714-010-1071-8

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