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

TL;DR

This paper explores how smoothing the velocity profile in an analogue fluid model of AdS2 spacetime removes the need for extra boundary conditions, linking fluid regularization to spacetime deformations.

Contribution

It demonstrates that smoothing the fluid velocity profile eliminates the boundary condition requirement, connecting fluid regularization with deformations of AdS2 spacetime.

Findings

Smoothing the velocity profile removes the need for extra boundary conditions.

Regularization corresponds to deformations of AdS2 near spatial infinity.

Both models agree in the long wavelength limit after regularization.

Abstract

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