Topological Phase Transitions in Superfluids Near Black Hole Horizons

We investigate a two-dimensional superfluid model confined to the equatorial 2 + 1 slice of a 3 + 1 black-hole spacetime. We adapt the 2D XY model to curved backgrounds and analyze how the superfluid responds to variations in the black hole temperature. Our simulations show that vortex–antivortex pairs proliferate as the system undergoes a topological phase transition. In the Schwarzschild–de Sitter case, the density of vortex–antivortex pairs increases near both the event and the cosmological horizons, and the critical temperature approaches zero at the horizons