Holographic superfluid sound modes with bulk acoustic black hole

The sound modes of a flowing superfluid can be characterized by the massless Klein-Gordon equation in an effective background metric. This metric can be engineered to mimic a black hole by incorporating an acoustic horizon. In this study, we explore the AdS/CFT dual of sound modes within a fluid exhibiting an acoustic horizon in the bulk. Focusing on fluids with purely radial flow, we derive the effective metric for the acoustic spacetime and establish necessary conditions for the existence of an acoustic black hole geometry within the fluid. We examine two examples of acoustic black holes embedded in pure anti-de Sitter spacetime. For both examples, we compute the effective Hawking temperature associated with the bulk acoustic horizon and investigate the near-horizon properties. We then derive the superfluid velocity profile that may lead to infrared emergent quantum criticality. Our calculations reveal that although the superfluid is at zero temperature, the sound modes experience an effective nonzero temperature due to the presence of an acoustic horizon. We also calculate the retarded Green's function and the spectral density of the sound modes. Our findings reveal that the spectral density is gapless, while the retarded Green's functions display branch cuts rather than poles, a hallmark of strongly coupled systems. These calculations demonstrate how the behavior of sound modes in a fluid can deviate from that of the underlying scalar field, due to the deformation of the background metric into an effective one. Importantly, the detailed behavior of these modes in the presence of an acoustic horizon is contingent upon the specific fluid velocity profile.