Topological Phase Transitions in Superfluids Near Black Hole Horizons

We investigated a two-dimensional superfluid model immersed in a black hole spacetime and hypothesize that if a black hole collides with a thin superfluid film, it will trigger a topological phase transition within the superfluid, characterized by the production of vortex--antivortex pairs. We adapted the 2D XY model to a curved spacetime and elucidated the topological phase transition in response to variations in the black hole's temperature. Specializing the model to a Schwarzschild--de Sitter black hole, we found a proliferation of vortex--antivortex pairs close to the event and cosmological horizons.