Advertisement

Dynamics of the dissipative gravitational collapse in Einstein-Gauss-Bonnet gravity

  • G. AbbasEmail author
  • M. Tahir
Regular Article
  • 31 Downloads

Abstract.

In this work, we have investigated the effects of dissipation on the dynamics of a collapsing sphere with heat flux in 5-dimensional Einstein-Gauss-Bonnet gravity. For this purpose, the field equations as well as mass function have been formulated in the 5-dimensional Einstein-Gauss-Bonnet theory of gravity. The Misner-Sharp approach has been implemented to derive the dynamical equations in the form of proper time and radial derivatives in 5-dimensional Einstein-Gauss-Bonnet gravity. We have explored the impact of heat flux on the dynamical collapse of a spherical source. In the context of the Israel-Stewart theory, the heat transport equations are modeled to determine the impacts of radial heat flux with the assumption that in some approximations one may neglect the thermodynamics heat/viscous coupling coefficients. Further, the dynamical equations have been coupled withthe heat transport equation, and the consequences of such equation with the Gauss-Bonnet coupling constant \( \alpha\) have been discussed in detail.

References

  1. 1.
    S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1979)Google Scholar
  2. 2.
    J.R. Oppenheimer, H. Snyder, Phys. Rev. 56, 455 (1939)CrossRefGoogle Scholar
  3. 3.
    S. Chandrashekhar, Astrophys. J. 140, 417 (1964)MathSciNetCrossRefGoogle Scholar
  4. 4.
    L. Herrera, N.O. Santos, G. Le Denmat, Mon. Not. R. Astron. Soc. 237, 257 (1989)CrossRefGoogle Scholar
  5. 5.
    L. Herrera, N.O. Santos, Phys. Rep. 286, 53 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    L. Herrera, N.O. Santos, Mon. Not. R. Astron. Soc. 343, 1207 (2003)CrossRefGoogle Scholar
  7. 7.
    C.W. Misner, D. Sharp, Phys. Rev. B 136, 571 (1964)CrossRefGoogle Scholar
  8. 8.
    L. Herrera, N.O. Santos, G. Le Denmat, Gen. Relativ. Gravit. 44, 1143 (2012)CrossRefGoogle Scholar
  9. 9.
    C.W. Misner, D. Sharp, Phys. Rev. B 137, 1360 (1965)CrossRefGoogle Scholar
  10. 10.
    L. Herrera, A. Di Prisco, J. Hernández-Pastora, N.O. Santo, Phys. Lett. A 237, 113 (1998)CrossRefGoogle Scholar
  11. 11.
    L. Herrera, N.O. Santos, Phys. Rev. D 70, 084004 (2004)MathSciNetCrossRefGoogle Scholar
  12. 12.
    L. Herrera, A. Di Prisco, J. Ospino, Gen. Relativ. Gravit. 44, 2645 (2012)CrossRefGoogle Scholar
  13. 13.
    L. Herrera, Int. J. Mod. Phys. D 15, 2197 (2006)CrossRefGoogle Scholar
  14. 14.
    L. Herrera, N.O. Santos, A. Wang, Phys. Rev. D 78, 084026 (2008)CrossRefGoogle Scholar
  15. 15.
    G. Abbas, H. Nazar, Eur. Phys. J. C 78, 510 (2018)CrossRefGoogle Scholar
  16. 16.
    S.M. Shah, G. Abbas, Astrophys, Space Sci. 363, 176 (2018)CrossRefGoogle Scholar
  17. 17.
    S.M. Shah, G. Abbas, Eur. Phys. J. C 77, 251 (2017)CrossRefGoogle Scholar
  18. 18.
    G. Abbas, M.S. Khan, Z. Ahmad, M. Zubair, Eur. Phys. J. C 77, 443 (2017)CrossRefGoogle Scholar
  19. 19.
    G. Abbas et al., Iran J. Sci. Technol. Trans. Sci. 42, 1659 (2018)CrossRefGoogle Scholar
  20. 20.
    M. Sharif, M. Azam, Chin. Phys. B 22, 050401 (2013)CrossRefGoogle Scholar
  21. 21.
    M. Sharif, G. Abbas, Astrophys. Space Sci. 327, 285 (2010)CrossRefGoogle Scholar
  22. 22.
    M. Sharif, Z. Ahamd, Mod. Phys. Lett. A 22, 1493 (2007)CrossRefGoogle Scholar
  23. 23.
    M. Sharif, Z. Ahamd, Mod. Phys. Lett. A 22, 2947 (2007)CrossRefGoogle Scholar
  24. 24.
    M. Sharif, Z. Ahamd, J. Korean Phys. Soc. 52, 980 (2008)CrossRefGoogle Scholar
  25. 25.
    M. Sharif, Z. Ahamd, Acta Phys. Pol. B 39, 1337 (2008)Google Scholar
  26. 26.
    M. Sharif, Z. Yousaf, Eur. Phys. J. C 73, 2633 (2013)CrossRefGoogle Scholar
  27. 27.
    M. Sharif, Z. Yousaf, Mon. Not. R. Astron. Soc. 440, 3479 (2014)CrossRefGoogle Scholar
  28. 28.
    M. Sharif, M.Z. Bhatti, J. Cosmol. Astropart. Phys. 11, 014 (2013)CrossRefGoogle Scholar
  29. 29.
    M. Sharif, M.Z. Bhatti, Astropart. Phys. 56, 35 (2014)CrossRefGoogle Scholar
  30. 30.
    A. Mitra, Phys. Rev. D 74, 024010 (2006)CrossRefGoogle Scholar
  31. 31.
    J. Lattimer, Nucl. Phys. A 478, 199 (1988)CrossRefGoogle Scholar
  32. 32.
    S.M. Shah, G. Abbas, Eur. Phys. J. A 53, 228 (2017)CrossRefGoogle Scholar
  33. 33.
    L. Herrera, A. Di Prisco, E. Fuenmayor, O. Troconis, Int. J. Mod. Phys. D 18, 129 (2009)CrossRefGoogle Scholar
  34. 34.
    M.B. Green, J.H. Schward, Phys. Lett. B 149, 117 (1984)MathSciNetCrossRefGoogle Scholar
  35. 35.
    D.J. Gross, J. Harvey, E. Martinec, R. Rohm, Phys. Rev. Lett. 6, 502 (1985)CrossRefGoogle Scholar
  36. 36.
    B. Zwiebach, Phys. Lett. B 156, 315 (1985)CrossRefGoogle Scholar
  37. 37.
    D.G. Boulware, S. Deser, Phys. Rev. Lett. 55, 2656 (1985)CrossRefGoogle Scholar
  38. 38.
    F. Tangherlini, Nuovo Cimento 27, 636 (1963)MathSciNetCrossRefGoogle Scholar
  39. 39.
    R.C. Myers, M.J. Perry, Ann. Phys. 172, 304 (1986)CrossRefGoogle Scholar
  40. 40.
    G. Abbas, S. Sawar, Astrophys. Space Sci. 357, 23 (2015)CrossRefGoogle Scholar
  41. 41.
    G. Abbas, M. Zubair, Mod. Phys. Lett. A 30, 1550038 (2015)CrossRefGoogle Scholar
  42. 42.
    I. Antoniadis, J. Rizos, K. Tamvakis, Nucl. Phys. B 415, 497 (1994)CrossRefGoogle Scholar
  43. 43.
    P. Kanti, J. Rizos, K. Tamvakis, Phys. Rev. D 59, 083512 (1999)MathSciNetCrossRefGoogle Scholar
  44. 44.
    P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 54, 5049 (1996)MathSciNetCrossRefGoogle Scholar
  45. 45.
    P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 57, 6255 (1998)MathSciNetCrossRefGoogle Scholar
  46. 46.
    T. Torii, H. Yajima, K.I. Maeda, Phys. Rev. D 55, 739 (1997)MathSciNetCrossRefGoogle Scholar
  47. 47.
    R.G. Cai, Phys. Rev. D 65, 084014 (2002)MathSciNetCrossRefGoogle Scholar
  48. 48.
    J.T. Wheeler, Nucl. Phys. B 268, 737 (1986)CrossRefGoogle Scholar
  49. 49.
    M. Zubair, H. Azmat, I. Noureen, Eur. Phys. J. C 77, 169 (2017)CrossRefGoogle Scholar
  50. 50.
    G. Abbas, R. Ahmed, Eur. Phys. J. C 77, 441 (2017)CrossRefGoogle Scholar
  51. 51.
    G. Abbas, M. Zubair, Mod. Phys. Lett. A 30, 1550038 (2015)CrossRefGoogle Scholar
  52. 52.
    D. Ida, K. Nakao, Phys. Rev. D 66, 064026 (2002)MathSciNetCrossRefGoogle Scholar
  53. 53.
    S. Jhingan, S.G. Ghosh, Phys. Rev. D 81, 024010 (2010)CrossRefGoogle Scholar
  54. 54.
    S.D. Maharaj, B. Chilambwe, S. Hansraj, Phys. Rev. D 91, 084049 (2015)MathSciNetCrossRefGoogle Scholar
  55. 55.
    G. Abbas, M. Tahir, Eur. Phys. J. C 77, 537 (2017)CrossRefGoogle Scholar
  56. 56.
    A. Banerjee, A. Sil, S. Chatterjee, Gen. Relativ. Gravit. 26, 999 (1994)CrossRefGoogle Scholar
  57. 57.
    S.G. Ghosh, A. Banerjee, Int. J. Mod. Phys. D 12, 639 (2003)CrossRefGoogle Scholar
  58. 58.
    S.G. Ghosh, D.W. Deshkar, N.N. Saste, Int. J. Mod. Phys. D 16, 53 (2007)CrossRefGoogle Scholar
  59. 59.
    I. Müller, Z. Phys. 198, 329 (1967)CrossRefGoogle Scholar
  60. 60.
    W. Israel, Ann. Phys. (N.Y.) 100, 310 (1976)CrossRefGoogle Scholar
  61. 61.
    W. Israel, J. Stewart, Ann. Phys. (N.Y.) 118, 341 (1979)CrossRefGoogle Scholar
  62. 62.
    C. Cattaneo, Atti Semin. Mat. Fis. Univ. Modena 3, 3 (1948)Google Scholar
  63. 63.
    H. Maeda, Class. Quantum Grav. 23, 2155 (2006)CrossRefGoogle Scholar
  64. 64.
    L. Herrera, A. Di Prisco, J. Hernández-Pastora, J. Martín, J. Martínez, Class. Quantum Grav. 14, 2239 (1997)CrossRefGoogle Scholar
  65. 65.
    L. Herrera, Phys. Lett. A 300, 157 (2002)CrossRefGoogle Scholar
  66. 66.
    J.J. Schwarz, Nucl. Phys. B 226, 269 (1983)CrossRefGoogle Scholar
  67. 67.
    C.B. Collins, J. Math. Phys. 18, 2116 (1977)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe Islamia University of BahawalpurBahawalpurPakistan

Personalised recommendations