On the geometry outside of acoustic black holes in $2+1$-dimensional spacetime

TL;DR

This paper explores the geometry outside acoustic black holes in 2+1 dimensions, analyzing test particle and wave behaviors, revealing effects analogous to general relativity, with implications for future experimental verification.

Contribution

It investigates the orbits and time delays of vortices and sound waves in 2+1D acoustic black hole spacetime, highlighting effects similar to those in general relativity.

Findings

Lyapunov exponent saturates chaos bound for infalling vortices

Vortex and sound wave orbits resemble relativistic effects

Time delay of sound matches predictions of curved spacetime effects

Abstract

Analogue black holes, which can mimic the kinetic aspects of real black holes, have been proposed for many years. The growth of the radial momentum of test particles toward the acoustic horizon is calculated for acoustic black holes in flat and curved spacetimes. Surprisingly, for a freely infalling vortex approaching the acoustic black hole, the Lyapunov exponent of the growth of the momentum at the horizon saturates the chaos bound $\Lambda_{\rm Lyapunov}\leq 2 \pi T$. We investigate the orbits of test vortices and sound wave rays in the $2+1$-dimensional "curved" spacetime of an acoustic black hole. We show that the vortices orbit, the sound wave orbit, and the time delay of sound are similar to those famous effects of general relativity. These effects can be verified experimentally in future experiments.