Hydraulic jump as a white hole

  • G. E. Volovik
Gravity, Astrophysics


In the geometry of the circular hydraulic jump, the velocity of the liquid in the interior region exceeds the speed of the capillary-gravity waves (ripplons), whose spectrum is “relativistic” in the shallow water limit. The velocity flow is radial and outward, and thus the relativistic ripplons cannot propagate into the interior region. In terms of the effective 2 + 1 dimensional Painlevé-Gullstrand metric appropriate for the propagating ripplons, the interior region imitates a white hole. The hydraulic jump represents the physical singularity at the white-hole horizon. The instability of the vacuum in the ergoregion inside the circular hydraulic jump and its observation in recent experiments on superfluid 4He by Rolley et al. [3] are discussed.

PACS numbers

04.70.−s 67.40.Hf 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981).CrossRefADSGoogle Scholar
  2. 2.
    C. Barcelo, S. Liberati, and M. Visser, gr-qc/0505065.Google Scholar
  3. 3.
    E. Rolley, C. Guthmann, M. S. Pettersen, and C. Chevallier, in Proceedings of the 24th Conference on Low Temperature Physics (in press); physics/0508200.Google Scholar
  4. 4.
    R. Schützhold and W. G. Unruh, Phys. Rev. D 66, 044019 (2002).Google Scholar
  5. 5.
    G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).Google Scholar
  6. 6.
    G. E. Volovik, JETP Lett. 75, 418 (2002); cond-mat/0202445; JETP Lett. 76, 240 (2002); gr-qc/0208020.ADSGoogle Scholar
  7. 7.
    R. Blaauwgeers, V. B. Eltsov, G. Eska, et al., Phys. Rev. Lett. 89, 155301 (2002).Google Scholar
  8. 8.
    R. Schützhold and W. G. Unruh, Phys. Rev. Lett. 95, 031301 (2005).Google Scholar
  9. 9.
    L. Rayleigh, Proc. R. Soc. London, Ser. A 90, 324 (1914).ADSzbMATHGoogle Scholar
  10. 10.
    C. Ellegaard, A. E. Hansen, A. Haaning, et al., Nature 392, 767 (1998); Nonlinearity 12, 1 (1999).CrossRefADSGoogle Scholar
  11. 11.
    P. Painlevé, C. R. Acad. Sci. 173, 677 (1921); A. Gullstrand, Ark. Mat., Astron. Fys. 16 (8), 1 (1922).Google Scholar
  12. 12.
    A. J. S. Hamilton and J. P. Lisle, gr-qc/0411060; M. Visser and A. Nielsen, gr-qc/0510083.Google Scholar
  13. 13.
    T. Vachaspati, J. Low Temp. Phys. 136, 361 (2004).CrossRefGoogle Scholar
  14. 14.
    Ü. Parts, V. M. H. Ruutu, J. H. Koivuniemi, et al., Europhys. Lett. 31, 449 (1995).Google Scholar
  15. 15.
    A. Vorontsov and J. A. Sauls, J. Low Temp. Phys. 134, 1001 (2004); cond-mat/0309599.CrossRefGoogle Scholar
  16. 16.
    Seamus Davis, private communication at NEDO 2nd International Workshop on Quantum Fluids and Solids (Hawaii, 1999).Google Scholar
  17. 17.
    T. Bohr, P. Dimon, and V. Putkaradge, J. Fluid Mech. 254, 635 (1993); T. Bohr, C. Ellegaard, A. E. Hansen, and A. Haaning, Physica B (Amsterdam) 228, 1 (1996).ADSGoogle Scholar
  18. 18.
    S. B. Singha, J. K. Bhattacharjee, and A. K. Ray, cond-mat/0508388.Google Scholar
  19. 19.
    S. Corley and T. Jacobson, Phys. Rev. D 59, 124011 (1999).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2005

Authors and Affiliations

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

Personalised recommendations