Advertisement

Fermionic microstates within the Painlevé-Gullstrand black hole

  • P. Huhtala
  • G. E. Volovik
Gravitation, Astrophysics

Abstract

We consider the quantum vacuum of a fermionic field in the presence of a black hole background as a possible candidate for the stabilized black hole. The stable vacuum state (as well as thermal equilibrium states at an arbitrary temperature) can exist if we use the Painlevé-Gullstrand description of the black hole and the superluminal dispersion of the particle spectrum at high energy, which is introduced in the free-falling frame. This choice is inspired by the analogy between the quantum vacuum and the ground state of quantum liquid, in which the event horizon for the low-energy fermionic quasiparticles can also arise. The quantum vacuum is characterized by the Fermi surface that appears behind the event horizon. We do not consider the back reaction, and therefore, there is no guarantee that the stable black hole exists. But if it does exist, the Fermi surface behind the horizon would be the necessary attribute of its vacuum state. We also consider the exact discrete spectrum of fermions inside the horizon, which allows us to discuss the problem of fermion zero modes.

Keywords

Black Hole Fermi Surface Vacuum State Event Horizon Zero Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981); Phys. Rev. D 51, 2827 (1995).CrossRefADSGoogle Scholar
  2. 2.
    T. Jacobson and G. E. Volovik, Phys. Rev. D 58, 064021 (1998).Google Scholar
  3. 3.
    L. J. Garay, J. R. Anglin, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 85, 4643 (2000); Phys. Rev. A 63, 023611 (2001).CrossRefADSGoogle Scholar
  4. 4.
    G. Chapline, E. Hohlfeld, R. B. Laughlin, and D. I. Santiago, Philos. Mag. B 81, 235 (2001).Google Scholar
  5. 5.
    R. Laughlin and D. Pines, Proc. Natl. Acad. Sci. USA 97, 28 (2000).ADSMathSciNetGoogle Scholar
  6. 6.
    G. E. Volovik, Phys. Rep. 351, 195 (2001).CrossRefADSMATHMathSciNetGoogle Scholar
  7. 7.
    S. W. Hawking, Nature 248, 30 (1974).CrossRefADSGoogle Scholar
  8. 8.
    G. E. Volovik, Phys. Lett. A 142, 282 (1989).CrossRefADSGoogle Scholar
  9. 9.
    S. Corley and T. Jacobson, Phys. Rev. D 54, 1568 (1996).CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    S. Corley, Phys. Rev. D 57, 6280 (1998).ADSMathSciNetGoogle Scholar
  11. 11.
    S. Corley and T. Jacobson, Phys. Rev. D 59, 124011 (1999).Google Scholar
  12. 12.
    A. Starobinsky, Pis’ma Zh. Éksp. Teor. Fiz. 73, 415 (2001) [JETP Lett. 73, 371 (2001)].Google Scholar
  13. 13.
    T. Jacobson, gr-qc/0110079; T. Jacobson and D. Mattingly, Phys. Rev. D 63, 041502 (2001); gr-qc/0007031.Google Scholar
  14. 14.
    P. O. Mazur and E. Mottola, gr-qc/0109035.Google Scholar
  15. 15.
    M. Mohazzab, J. Low Temp. Phys. 121, 659 (2000).Google Scholar
  16. 16.
    G. E. Volovik, Pis’ma Zh. Éksp. Teor. Fiz. 70, 717 (1999) [JETP Lett. 70, 711 (1999)].Google Scholar
  17. 17.
    P. Painlevé and C. R. Hebd, Acad. Sci., Paris 173, 677 (1921); A. Gullstrand, Ark. Mat., Astron. Fys. 16, 1 (1922).Google Scholar
  18. 18.
    P. Kraus and F. Wilczek, Mod. Phys. Lett. A 9, 3713 (1994).ADSMathSciNetGoogle Scholar
  19. 19.
    K. Martel and E. Poisson, Am. J. Phys. 69, 476 (2001).CrossRefADSGoogle Scholar
  20. 20.
    R. Schützhold, Phys. Rev. D 64, 024029 (2001).Google Scholar
  21. 21.
    M. K. Parikh and F. Wilczek, Phys. Rev. Lett. 85, 5042 (2000).CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    C. Doran, Phys. Rev. D 61, 067503 (2000).Google Scholar
  23. 23.
    M. Visser, Class. Quantum Grav. 15, 1767 (1998).CrossRefADSMATHMathSciNetGoogle Scholar
  24. 24.
    S. Liberati, S. Sonego, and M. Visser, Class. Quantum Grav. 17, 2903 (2000).CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    M. Stone, cond-mat/0012316.Google Scholar
  26. 26.
    M. Sakagami and A. Ohashi, gr-qc/0108072.Google Scholar
  27. 27.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 2: The Classical Theory of Fields (Nauka, Moscow, 1973; Pergamon, Oxford, 1975).Google Scholar
  28. 28.
    G. E. Volovik, Pis’ma Zh. Éksp. Teor. Fiz. 73, 721 (2001) [JETP Lett. 73, 637 (2001)].Google Scholar
  29. 29.
    S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).Google Scholar
  30. 30.
    W. H. Zurek and Don N. Page, Phys. Rev. D 29, 628 (1984).CrossRefADSGoogle Scholar
  31. 31.
    G. ’t Hooft, Nucl. Phys. (Proc. Suppl.) 68, 174 (1998).ADSMathSciNetGoogle Scholar
  32. 32.
    A. D. Sakharov, Dokl. Akad. Nauk SSSR 177, 70 (1967) [Sov. Phys. Dokl. 12, 1014 (1968)].Google Scholar
  33. 33.
    T. Jacobson, gr-qc/9404039.Google Scholar
  34. 34.
    J. D. Bekenstein, in Proceedings of the 8th Marcel Grossman Meeting, Ed. by Tsvi Piran (World Sci., Singapore, 1999); gr-qc/9710076.Google Scholar
  35. 35.
    H. A. Kastrup, Phys. Lett. B 413, 267 (1997).ADSMathSciNetGoogle Scholar
  36. 36.
    V. F. Mukhanov, Pis’ma Zh. Éksp. Teor. Fiz. 44, 78 (1986) [JETP Lett. 44, 63 (1986)].MathSciNetGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • P. Huhtala
    • 1
  • G. E. Volovik
    • 1
    • 2
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyFinland
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

Personalised recommendations