Non-linear effects in time-dependent transonic flows: An analysis of analogue black hole stability

TL;DR

This paper investigates the dynamical behaviors and stability of transonic flows in atomic condensates using the Gross-Pitaevskii equation, revealing how black hole analogues stabilize over time and white hole analogues develop undulations or solitons.

Contribution

It provides a detailed analysis of time-dependent transonic flows, identifying stability properties and dynamical instabilities in black hole and white hole analogues within atomic condensates.

Findings

Black hole analogues settle into stationary profiles obeying a no hair theorem.

White hole analogues develop macroscopic undulations or emit solitons.

Flows crossing the sound speed twice exhibit complex instability behaviors.

Abstract

We study solutions of the one-dimensional Gross-Pitaevskii equation to better understand dynamical instabilities occurring in flowing atomic condensates. Whereas transonic stationary flows can be fully described in simple terms, time-dependent flows exhibit a wide variety of behaviors. When the sound speed is crossed once, we observe that flows analogous to black holes obey something similar to the so-called no hair theorem since their late time profile is stationary and uniquely fixed by parameters entering the Hamiltonian and conserved quantities. For flows analogous to white holes, at late time one finds a macroscopic undulation in the supersonic side which has either a fixed amplitude, or a widely varying one signaling a quasi periodic emission of solitons on the subsonic side. When considering flows which cross the sound speed twice, we observe various scenarios which can be understood from the above behaviors, and from the hierarchy of the growth rates of the dynamical instabilities characterizing such flows.