Astrophysics and Space Science

, Volume 347, Issue 1, pp 71–76 | Cite as

Plane symmetric gravitational collapse and linear equation of state

Original Article

Abstract

This paper examines the gravitational collapse in plane symmetry with a perfect fluid using a linear equation of state p=. We find a class of collapse models satisfying the Einstein field equations and also the regularity as well as energy conditions. For a given initial data, the outcome of the collapse turns out to be a black membrane or a naked singularity depending upon the equation of state parameter. We conclude that this parameter plays a crucial role in determining the final fate of the collapse.

Keywords

Gravitational collapse Equation of state Plane symmetry 

References

  1. Bronnikov, K.A.: Gen. Relativ. Gravit. 15, 823 (1983) MathSciNetADSCrossRefGoogle Scholar
  2. Bronnikov, K.A., Kovalchuk, M.A.: Probl. Teor. Gravit. Elem. Chast. 11, 131 (1980) (in Russian) MathSciNetADSGoogle Scholar
  3. Bronnikov, K.A., Kovalchuk, M.A.: Gen. Relativ. Gravit. 15, 809 (1983) MathSciNetADSCrossRefGoogle Scholar
  4. Bronnikov, K.A., Kovalchuk, M.A.: Gen. Relativ. Gravit. 16, 15 (1984) MathSciNetADSCrossRefGoogle Scholar
  5. Chan, R.: Mon. Not. R. Astron. Soc. 316, 588 (2000) ADSCrossRefGoogle Scholar
  6. Di Prisco, A., Herrera, L., MacCallum, M.A.H., Santos, N.O.: Phys. Rev. D 80, 064031 (2009) MathSciNetADSCrossRefGoogle Scholar
  7. Ghosh, S.G.: Int. J. Mod. Phys. A 23, 4245 (2008) ADSMATHCrossRefGoogle Scholar
  8. Ghosh, S.G., Deshkar, D.W.: Int. J. Mod. Phys. D 12, 317 (2003) MathSciNetADSCrossRefGoogle Scholar
  9. Goswami, R.: 0707.1122 [gr-qc] (2007)
  10. Goswami, R., Joshi, P.S.: Class. Quantum Gravity 19, 5229 (2002) MathSciNetADSMATHCrossRefGoogle Scholar
  11. Goswami, R., Joshi, P.S.: Class. Quantum Gravity 21, 3645 (2004a) MathSciNetADSMATHCrossRefGoogle Scholar
  12. Goswami, R., Joshi, P.S.: Phys. Rev. D 69, 064027 (2004b) MathSciNetADSCrossRefGoogle Scholar
  13. Goswami, R., Joshi, P.S., Vaz, C., Witten, L.: Phys. Rev. D 70, 084038 (2004c) MathSciNetADSCrossRefGoogle Scholar
  14. Hayward, S.A.: Class. Quantum Gravity 17, 1749 (2000) MathSciNetADSMATHCrossRefGoogle Scholar
  15. Joshi, P.S., Dwivedi, I.H.: Commun. Math. Phys. 146, 333 (1992) MathSciNetADSMATHCrossRefGoogle Scholar
  16. Kurita, Y., Nakao, K.: Phys. Rev. D 73, 064002 (2006) MathSciNetADSCrossRefGoogle Scholar
  17. Lake, K.: Phys. Rev. D 62, 027301 (2000) MathSciNetADSCrossRefGoogle Scholar
  18. Markovic, D., Shapiro, S.L.: Phys. Rev. D 61, 084029 (2000) ADSCrossRefGoogle Scholar
  19. Misner, C.W., Sharp, D.: Phys. Rev. 136, b571 (1964) MathSciNetADSCrossRefGoogle Scholar
  20. Nakao, K., Morisawa, Y.: Phys. Rev. D 71, 124007 (2005a) MathSciNetADSCrossRefGoogle Scholar
  21. Nakao, K., Morisawa, Y.: Prog. Theor. Phys. 113, 73 (2005b) ADSMATHCrossRefGoogle Scholar
  22. Nath, S., Debnathm, U., Chakraborty, S.: Astrophys. Space Sci. 313, 431 (2008) ADSMATHCrossRefGoogle Scholar
  23. Nolan, B.C.: Phys. Rev. D 60, 024014 (1999) MathSciNetADSCrossRefGoogle Scholar
  24. Nolan, B.C.: Phys. Rev. D 65, 104006 (2002) MathSciNetADSCrossRefGoogle Scholar
  25. Oppenheimer, J.R., Snyder, H.: Phys. Rev. 56, 455 (1939) ADSMATHCrossRefGoogle Scholar
  26. Ori, A., Piran, T.: Phys. Rev. Lett. 59, 2137 (1987) ADSCrossRefGoogle Scholar
  27. Ori, A., Piran, T.: Gen. Relativ. Gravit. 20, 7 (1988) MathSciNetADSMATHCrossRefGoogle Scholar
  28. Ori, A., Piran, T.: Phys. Rev. D 42, 1068 (1990) MathSciNetADSCrossRefGoogle Scholar
  29. Oron, A.: Phys. Rev. D 66, 023006 (2002) ADSCrossRefGoogle Scholar
  30. Penrose, R.: Nuovo Cimento 1, 252 (1969) Google Scholar
  31. Pereira, P.R.C.T., Wang, A.: Int. J. Mod. Phys. D 11, 561 (2002) MathSciNetADSMATHCrossRefGoogle Scholar
  32. Pereira, P.R.C.T., Wang, A.: Phys. Rev. D 62, 124001 (2003) ADSCrossRefGoogle Scholar
  33. Sarwe, S., Saraykar, R.V., Joshi, P.S.: arXiv:1207.3200 (2012)
  34. Sharif, M., Ahmad, Z.: Mod. Phys. Lett. A 22, 1493 (2007a) MathSciNetADSMATHCrossRefGoogle Scholar
  35. Sharif, M., Ahmad, Z.: Gen. Relativ. Gravit. 39, 1331 (2007b) MathSciNetADSMATHCrossRefGoogle Scholar
  36. Sharif, M., Ahmad, Z.: Int. J. Mod. Phys. A 23, 181 (2008) MathSciNetADSMATHCrossRefGoogle Scholar
  37. Sharif, M., Siddiqa, A.: Mod. Phys. Lett. A 25, 2831 (2010) MathSciNetADSMATHCrossRefGoogle Scholar
  38. Sharif, M., Siddiqa, A.: Gen. Relativ. Gravit. 43, 73 (2011) MathSciNetADSMATHCrossRefGoogle Scholar
  39. Singh, T.P.: Phys. Rev. D 58, 024004 (1998) MathSciNetADSCrossRefGoogle Scholar
  40. Wang, A., Wu, Y., Wu, Z.C.: Gen. Relativ. Gravit. 36, 1225 (2004) ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan

Personalised recommendations