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 Pis'ma v Zh. Èksper. Teoret. Fiz., 2002, Volume 76, Issue 5, Pages 296–300 (Mi jetpl2902)

GRAVITY, ASTROPHYSICS

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

G. E. Volovikab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Low Temperature Laboratory, Helsinki University of Technology

Abstract: An analog of black hole can be realized in the low-temperature laboratory. The horizon can be constructed for the «relativistic» ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, $^3$He-A and $^3$He-B, sliding along each other without friction. Similar experimental arrangement has been recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments corresponds to 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.

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English version:
Journal of Experimental and Theoretical Physics Letters, 2002, 76:5, 240–244

Document Type: Article
PACS: 04.50.+h, 04.70.Dy, 47.20.Ft, 67.57.De
Language: English

Citation: G. E. Volovik, “Black-hole horizon and metric singularity at the brane separating two sliding superfluids”, Pis'ma v Zh. Èksper. Teoret. Fiz., 76:5 (2002), 296–300; JETP Letters, 76:5 (2002), 240–244

Citation in format AMSBIB
\Bibitem{Vol02} \by G.~E.~Volovik \paper Black-hole horizon and metric singularity at the brane separating two sliding superfluids \jour Pis'ma v Zh. \Eksper. Teoret. Fiz. \yr 2002 \vol 76 \issue 5 \pages 296--300 \mathnet{http://mi.mathnet.ru/jetpl2902} \transl \jour JETP Letters \yr 2002 \vol 76 \issue 5 \pages 240--244 \crossref{https://doi.org/10.1134/1.1520613} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0041416402} `

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This publication is cited in the following articles:
1. JETP Letters, 81:12 (2005), 634–638
2. JETP Letters, 82:10 (2005), 624–627
3. Ge X.-H., Sun J.-R., Tian Yu., Wu X.-N., Zhang Yu.-L., “Holographic Interpretation of Acoustic Black Holes”, Phys. Rev. D, 92:8 (2015), 084052
4. Eltsov V.B. Gordeev A. Krusius M., “Kelvin-Helmholtz Instability of Ab Interface in Superfluid He-3”, Phys. Rev. B, 99:5 (2019), 054104
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