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

TL;DR

This paper proposes a laboratory analog of a black hole using superfluid interfaces, exploring horizon formation and metric singularities through shear-flow instabilities in superfluid 3He systems.

Contribution

It introduces a novel experimental setup to simulate black hole horizons and singularities using superfluid interfaces, linking fluid dynamics with gravitational analogs.

Findings

Observation of ergoregion formation in superfluid ripplons

Identification of conditions for black-hole event horizon analog

Analysis of metric singularity corresponding to Kelvin-Helmholtz instability

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, 3He-A and 3He-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 (cond-mat/0111343). The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments (cond-mat/0111343) 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.