Holographic homogeneous superfluid on the sphere

Abstract: In this paper, we extend the study of holographic superfluids from planar topology to spherical topology, inspired by recent studies on Bose-Einstein condensation (BEC) on shell-shaped geometry. We investigate the superfluid phase transition from normal fluid and its Quasi-Normal Modes (QNMs) on the sphere. It turns out that the critical temperature for the superfluid phase transition on the sphere is higher than that in the planar case. We investigated four different solutions in the backgrounds of large and small black holes. The calculation of free energy selects the most stable solution. Finally, after calculating the quasi-normal modes and their dynamic behavior, we obtained three different channels similar to the planar superfluid case, along with the ``first" hydrodynamic excitation mode.