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An analogue model for the $\text{AdS}_2$ spacetime has been recentlyintroduced by Mosna, Pitelli and Richartz [Phys. Rev. D 94, 104065 (2016)] byconsidering sound waves propagating on a fluid with an ill-defined velocityprofile at its source/sink. The wave propagation is then uniquely defined onlywhen one imposes an extra boundary condition at the source/sink (whichcorresponds to the spatial infinity of $\text{AdS}_2$). Here we show that, oncethis velocity profile is smoothed out at the source/sink, the need for extraboundary conditions disappears. This, in turn, corresponds to deformations ofthe $\text{AdS}_2$ spacetime near its spatial infinity. We also examine howthis regularization of the velocity profile picks up a specific boundarycondition for the idealized system, so that both models agree in the longwavelength limit.

Analogue gravity and radial fluid flows: The case of AdS and its deformations