No hair theorems for analogue black holes

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.

Final version published in PRD; a new figure illustrates the link with the relativistic regime, and another the stability of the results when considering larger non-linear perturbations; a few typos fixed

References in corpus (7)

• Measurement of stimulated Hawking emission in an analogue system
• Observation of negative-frequency waves in a water tank: A classical analogue to the Hawking effect?
• Black/White hole radiation from dispersive theories
• The theory of Hawking radiation in laboratory analogues
• Acoustic white holes in flowing atomic Bose-Einstein condensates
• Non-linear effects in time-dependent transonic flows: An analysis of analogue black hole stability
• Time-dependent study of a black-hole laser in a flowing atomic condensate

Cited by in corpus (8)

• Phonon spectrum and correlations in a transonic flow of an atomic Bose gas
• Assessing degrees of entanglement of phonon states in atomic Bose gases through the measurement of commuting observables
• Time-dependent study of a black-hole laser in a flowing atomic condensate
• Non-linear stationary solutions in realistic models for analog black-hole lasers
• Gravity waves on modulated flows downstream from an obstacle: The transcritical case
• Formation dynamics of black- and white-hole horizons in an analogue gravity model
• Black holes will break up solitons and white holes may destroy them
• Time Crystal from Self-Amplification of Spontaneous Analog Hawking Radiation