Black-hole horizon and metric singularity at the brane separating two sliding superfluids

  • G. E. Volovik
Gravity, Astrophysics


An analogue of a black hole can be realized in the low-temperature laboratory. The horizon can be constructed for “relativistic” ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, 3He-A and 3He-B, sliding along each other without friction. A similar experimental arrangement was recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] corresponds to the appearance of the ergoregion for ripplons. In the modified geometry, this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity—the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.

PACS numbers

04.50.+h 04.70.Dy 67.57.De 47.20.Ft 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Blaauwgeers, V. B. Eltsov, G. Eska, et al., Phys. Rev. Lett. 89, 155301 (2002).Google Scholar
  2. 2.
    R. Schützhold and W. G. Unruh, gr-qc/0205099.Google Scholar
  3. 3.
    G. E. Volovik, Phys. Rep. 351, 195 (2001); G. E. Volovik, Universe in a Helium Dropley, forthcoming book in Oxford University Press, Scholar
  4. 4.
    G. E. Volovik, Pis’ma Zh. Éksp. Teor. Fiz. 75, 491 (2002) [JETP Lett. 75, 418 (2002)]; cond-mat/0202445.Google Scholar
  5. 5.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1989), Sec. 62, Problem 3, p. 247.Google Scholar
  6. 6.
    N. B. Kopnin, Zh. Éksp. Teor. Fiz. 92, 2106 (1987) [Sov. Phys. JETP 65, 1187 (1987)].Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • G. E. Volovik
    • 1
    • 2
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyHUTFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations