2 00 2 Black - hole horizon and metric singularity at the brane separating two sliding superfluids

An analog of black hole can be realized in the low-temperature laboratory. The horizon can be constructed for the 'relativistic' rip-plons (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 [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] 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 1 the black hole, where the determinant of the effective metric becomes infinite. 1. Introduction. The first experimental realization of two superfluid liquids sliding along each other [1] gives a new tool for investigation of many physical phenomena related to different areas of physics (classical hydrodynam-ics, rotating Bose condensates, cosmology, brane physics, etc.). Here we discuss how this experimental arrangement can be modified in order to produce an analog of the black-hole event horizon and of the singularity in the effective Lorentzian metric experienced by the collective modes (ripplons) living on the brane (the interface separating two different superfluid vacua, 3 He-A and 3 He-B, which we further refer as the AB-brane). The idea of the experiment is similar to that discussed by Schützhold and Unruh [2], who suggested to use the gravity waves on the surface of a liquid flowing in a shallow basin. In the long-wavelength limit the energy spectrum of the surface modes becomes 'relativistic', which allows us to describe the propagating modes in terms of the effective Lorentzian metric. Here we discuss the modification of this idea to the case of the ripplons propagating along the membrane between two superfluids. There are many advantages when one uses the superfluid liquids instead of the conventional ones: (1) The superfluids can slide along each other without any friction until the …