Holographic superfluid sound modes with bulk acoustic black hole

The sound modes of a flowing superfluid is described by the massless Klein-Gordon equation in an effective background metric. This effective background metric can be designed to mimick a black hole using the acoustic horizon. In this work, we study the AdS/CFT dual of the sound modes in the presence of an acoustic horizon in the bulk. Focusing on fluids with a purely radial flow, we derive the metric tensor for the effective acoustic spacetime and deduce a necessary condition for an acoustic black hole geometry to exist within the fluid. Using specific examples of superfluid velocity profiles, we obtained the source, operator expectation value, Green's function, and spectral density of the dual field theory by solving for the asymptotic behavior of the sound modes near the AdS boundary. In all our examples, the sound modes remain gapless but the excitations are described by branch cuts, instead of poles, which is typical of strongly coupled systems. Furthermore, we calculate the effective Hawking temperature of the dual field theory associated with the bulk acoustic horizon. Lastly, we investigate the near horizon properties and derive the superfluid velocity profile that can give rise to an infrared emergent quantum criticality.