Analogue model for anti-de Sitter as a description of point sources in fluids

TL;DR

This paper presents an analogue fluid model simulating a non-globally hyperbolic spacetime, specifically AdS2×S1, illustrating how boundary conditions at the boundary relate to point sources and affect wave stability.

Contribution

It introduces a fluid-based analogue model for AdS spacetime, demonstrating the connection between boundary conditions, wave dynamics, and stability in a non-globally hyperbolic setting.

Findings

Wave equation matches AdS2×S1 spacetime

Boundary conditions correspond to point sources at r=0

Fluid stability depends on boundary condition choice

Abstract

We introduce an analogue model for a nonglobally hyperbolic spacetime in terms of a two-dimensional fluid. This is done by considering the propagation of sound waves in a radial flow with constant velocity. We show that the equation of motion satisfied by sound waves is the wave equation on $AdS_2\times S^1$. Since this spacetime is not globally hyperbolic, the dynamics of the Klein-Gordon field is not well defined until boundary conditions at the spatial boundary of $AdS_2$ are prescribed. On the analogue model end, those extra boundary conditions provide an effective description of the point source at $r=0$. For waves with circular symmetry, we relate the different physical evolutions to the phase difference between ingoing and outgoing scattered waves. We also show that the fluid configuration can be stable or unstable depending on the chosen boundary condition.