Topological Phase Transitions in Superfluids Near Black Hole Horizons

Abstract

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.

Figures (4)

• Figure 1: Vortices and antivortices in a window of $(1/6)^{th}$ the lattice size, for the flat case. The top image shows the streamline-density plot at a temperature below the critical point, where no pairs are present. The bottom graph displays two vortex--antivortex pairs at a temperature above the critical point.
• Figure 2: Specific heat as a function of black hole temperature, with each data set representing three distinct distances from the black hole's horizon, as indicated in the legend. The top graph illustrates the specific heat for a superfluid near the event horizon of a Schwarzschild black hole, while the bottom graph shows the specific heat at a distance from the cosmological horizon of a Schwarzschild--de Sitter black hole.
• Figure 3: Number of vortices as a function of temperature. Top: at a radius $r=1.2\,R_H$; Bottom: at $r=10\,R_H$.
• Figure 4: Spin stiffness. Top: at $r=1.2\,R_H$ from the event horizon; Bottom: farther from the horizon, at $r=10\,R_H$. The data points are connected with a line to guide the eye.