Sound propagation in an acoustic black hole embedded in anti-de Sitter space

Abstract

Sound waves in the bulk of certain fluids behave like massless scalar fields in an effective curved spacetime. We show that this remains true for the case of a scalar fluid embedded in pure anti-de Sitter space. 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. Finally, for a specific acoustic black hole geometry, we solve the corresponding Klein-Gordon equation for radially propagating sound modes and analyze its asymptotic behavior near the AdS boundary. This allows us to extract the source, operator expectation value, and Green's function of the dual field theory.