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Earliest stages of the nonequilibrium in axially symmetric, self-gravitating, dissipative fluids

L. Herrera*

A. Di Prisco†

J. Ospino‡

J. Carot§

  • Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, 1050 Caracas, Venezuela and Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, 37007 Salamanca, Spain

  • Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, 1050 Caracas, Venezuela

  • Departamento de Matemática Aplicada and Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, 37007 Salamanca, Spain

  • Departament de Física, Universitat Illes Balears, E-07122 Palma de Mallorca, Spain

  • *lherrera@usal.es
  • †alicia.diprisco@ciens.ucv.ve
  • ‡j.ospino@usal.es
  • §jcarot@uib.cat
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Phys. Rev. D 94, 064072 – Published 26 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.064072

Abstract

We report a study on axially and reflection symmetric dissipative fluids, just after its departure from hydrostatic and thermal equilibrium, at the smallest time scale at which the first signs of dynamic evolution appear. Such a time scale is smaller than the thermal relaxation time, the thermal adjustment time, and the hydrostatic time. It is obtained that the onset of nonequilibrium will critically depend on a single function directly related to the time derivative of the vorticity. Among all fluid variables (at the time scale under consideration), only the tetrad component of the anisotropic tensor in the subspace orthogonal to the four-velocity and the Killing vector of axial symmetry, shows signs of dynamic evolution. Also, the first step toward a dissipative regime begins with a nonvanishing time derivative of the heat flux component along the meridional direction. The magnetic part of the Weyl tensor vanishes (not so its time derivative), indicating that the emission of gravitational radiation will occur at later times. Finally, the decreasing of the effective inertial mass density, associated to thermal effects, is clearly illustrated.

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References (50)

  1. L. Herrera, A. Di Prisco, J. Ibáñez, and J. Ospino, Phys. Rev. D 87, 024014 (2013).
  2. L. Herrera, A. Di Prisco, J. Ibáñez, and J. Ospino, Phys. Rev. D 89, 084034 (2014).
  3. G. F. R. Ellis, in Proceedings of the International School of Physics “Enrico Fermi”, Course 47: General Relativity and Cosmology, edited by R. K. Sachs (Academic Press, New York, 1971).
  4. G. F. R. Ellis and H. van Ellst, arXiv:gr-qc/9812046v4.
  5. G. F. R. Ellis Gen. Relativ. Gravit. 41, 581 (2009).
  6. G. F. R. Ellis, R. Maartens, and M. A. H. MacCallum, Relativistic Cosmology (Cambridge University Press, Cambridge, England, 2012).
  7. R. Kippenhahn and A. Weigert, Stellar Structure and Evolution, (Springer Verlag, Berlin, 1990).
  8. C. Hansen and S. Kawaler, Stellar Interiors: Physical Principles, Structure and Evolution, (Springer Verlag, Berlin, 1994).
  9. L. Herrera, A. Di Prisco, J. Ospino, and J. Carot, Int. J. Mod. Phys. D 25, 1650036 (2016).
  10. A. Burrows and J. M. Lattimer, Astrophys. J. 307, 178 (1986).
  11. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Proc. R. Soc. A 269, 21 (1962).
  12. H. Stephani, D. Kramer, M. MacCallum, C. Honselaers, and E. Herlt, Exact Solutions to Einsteins Field Equations, 2nd ed. (Cambridge University Press, Cambridge, England, 2003).
  13. J. Carot, Classical Quantum Gravity 17, 2675 (2000).
  14. G. T. Carlson, Jr. and J. L. Safko, Ann. Phys. (N.Y.) 128, 131 (1980).
  15. L. Herrera, J. Ospino, A. Di Prisco, E. Fuenmayor, and O. Troconis, Phys. Rev. D 79, 064025 (2009).
  16. L. Bel, C. R. Hebd. Seances Acad. Sci. 247, 1094 (1958).
  17. L. Bel, Cahiers de Physique 16, 59 (1962); Gen. Relativ. Gravit. 32, 2047 (2000).
  18. A. García-Parrado Gómez-Lobo, Classical Quantum Gravity 25, 015006 (2008).
  19. L. Herrera, W. Barreto, J. Carot, and A. Di Prisco, Classical Quantum Gravity 24, 2645 (2007).
  20. R. Sachs, Proc. R. Soc. A 270, 103 (1962).
  21. C. Eckart, Phys. Rev. 58, 919 (1940).
  22. L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1959).
  23. D. Joseph and L. Preziosi, Rev. Mod. Phys. 61, 41 (1989).
  24. R. Maartens, arXiv:astro-ph/9609119.
  25. L. Herrera and D. Pavón, Physica A (Amsterdam), 307, 121 (2002).
  26. W. Hiscock and L. Lindblom, Ann. Phys. (N.Y.) 151, 466 (1983).
  27. I. Müller, Z. Phys. 198, 329 (1967).
  28. W. Israel, Ann. Phys. (N.Y.) 100, 310 (1976).
  29. W. Israel and J. Stewart, Phys. Lett. A 58, 213 (1976).
  30. W. Israel and J. Stewart, Ann. Phys. (N.Y.) 118, 341 (1979).
  31. D. Pavón, D. Jou, and J. Casas-Vázquez, Ann. Inst. Henri Poincare, Sect. A 36, 79 (1982).
  32. B. Carter, in Journées Relativistes, edited by M. Cahen, R. Debever, and J. Geheniau (Université Libre de Bruxelles, Bruxelles, 1976).
  33. C. Cattaneo, Atti Semin. Mat. Fis. Univ. Modena 3, 3 (1948).
  34. R. Tolman, Phys. Rev. 35, 904 (1930).
  35. L. Herrera, A. Di Prisco, J. Hernández-Pastora, J. Martín, and J. Martínez, Classical Quantum Gravity 14, 2239 (1997).
  36. L. Herrera, A. Di Prisco, and J. Martínez, Phys. Lett. A 243, 7 (1998).
  37. L. Herrera and J. Martínez, J. Math. Phys. (N.Y.), 39, 3260 (1998).
  38. L. Herrera, Phys. Lett. A 300, 157 (2002).
  39. L. Herrera and N. O. Santos, Phys. Rev. D 70, 084004 (2004).
  40. L. Herrera, A. Di Prisco, and W. Barreto, Phys. Rev. D 73, 024008 (2006).
  41. L. Herrera, Int. J. Mod. Phys. D 15, 2197 (2006).
  42. A. Di Prisco, L. Herrera, G. Le Denmat, M. A. H. MacCallum, and N. O. Santos, Phys. Rev. D 76, 064017 (2007).
  43. L. Herrera, A. Di Prisco, E. Fuenmayor, and O. Troconis, Int. J. Mod. Phys. D 18, 129 (2009).
  44. M. Sharif and Z. Rehmat, Gen. Relativ. Gravit. 42, 1795 (2010).
  45. M. Sharif and A. Siddiqa, Gen. Relativ. Gravit. 43, 73 (2011).
  46. M. Sharif and H. Tahir, Eur. Phys. J. Plus, 128, 146 (2013).
  47. M. Sharif and I. Nawazish, Astrophys. Space Sci. 351, 313 (2014).
  48. M. Sharif and M. Z. Ul Haq Bhatti, Mod. Phys. Lett. A 29, 1450165 (2014).
  49. L. Herrera, A. Di Prisco, J. Ospino, and J. Carot, Phys. Rev. D 91, 024010 (2015).
  50. L. Herrera, Gen. Relativ. Gravit. 46, 1654 (2014).

Outline

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Phys. Rev. D 94, 064072– Published 26 September, 2016
  • Received 23 March 2016

© 2016 American Physical Society

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