A superfluid near a black hole horizon encounters a thermal gradient set by the Hawking temperature. The Hawking radiation is too weak to detect directly, but its effect on a superfluid is a phase transition: if the local temperature exceeds the critical temperature for superfluidity, the ordered phase breaks down and vortex-antivortex pairs proliferate.
The paper models a two-dimensional superfluid film in the curved spacetime of a Schwarzschild-de Sitter black hole. The 2D XY model — the standard framework for superfluid phase transitions — is adapted to curved spacetime, with the metric entering through the kinetic energy of the phase field. The effective temperature varies with position, increasing near both the event horizon and the cosmological horizon.
Near each horizon, vortex-antivortex pairs proliferate. The density of pairs traces the effective temperature profile set by the spacetime geometry. The BKT transition — the topological phase transition where bound vortex pairs unbind — occurs at a location determined by where the Hawking temperature crosses the critical temperature. The superfluid orders in the region between the two horizons and disorders near each one.
The superfluid becomes a thermometer for spacetime geometry. The vortex distribution maps the effective temperature profile, which maps the metric. In principle, measuring the superfluid's topological defects reconstructs information about the horizons — not through gravitational wave detection or electromagnetic observation but through the superfluid's own phase structure. The black hole writes its temperature into the topology of the superfluid.