No hair theorems for analogue black holes

TL;DR

This paper demonstrates that analogue black holes in transonic flows obey no-hair theorems, showing stability of stationary flows and characterizing emitted waves, with implications for understanding black hole analogues.

Contribution

It establishes no-hair theorems for analogue black holes in fluid flows and provides analytical and numerical analysis of their stability and wave emission behaviors.

Findings

Stationary flows are stable and act as attractors.

Time-reversed flows are unstable and emit solitons or undulations.

Analytical characterization of emitted waves matches numerical simulations.

Abstract

We show that transonic one dimensional flows which are analogous to black holes obey no-hair theorems both at the level of linear perturbations and in non-linear regimes. Considering solutions of the Gross-Pitaevskii (or Korteweg-de Vries) equation, we show that stationary flows which are asymptotically uniform on both sides of the horizon are stable and act as attractors. Using Whitham's modulation theory, we analytically characterize the emitted waves when starting from uniform perturbations. Numerical simulations confirm the validity of this approximation and extend the results to more general perturbations and to the (non-integrable) cubic-quintic Gross-Pitaevskii equation. When considering time reversed flows that correspond to white holes, the asymptotically uniform flows are unstable to sufficiently large perturbations and emit either a macroscopic undulation in the supersonic side, or a non-linear superposition of soliton trains.