The hydraulic jump as a white hole
G. E. Volovik
Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland
L. D. Landau Institute for Theoretical Physics, 117334 Moscow, Russia
PACS: 04.70.-s, 67.40.Hf
In the geometry of the circular hydraulic
jump, the velocity of the liquid in the interior region
exceeds the speed of 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 the 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, Guthmann, Pettersen and Chevallier
[10vol-Pettersen] are discussed.