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arXiv:2607.11396 · Physical review. D/Physical review. D.

Sonic black holes with thick horizons in BECs

Daniel Peñalver, Marco De Vito, Roberto Balbinot, Alessandro Fabbri

Published Sep 3, 2026• 0 citations
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Abstract

We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous. We shall concentrate on the case in which an extended sonic region is present, i.e. a region where the flow velocity equals exactly the speed of sound. These models can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.

DOI
10.1103/8hsh-96jl

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We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous. We shall concentrate on the case in which an extended sonic region is present, i.e. a region where the flow velocity equals exactly the speed of sound. These models can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.
In a previous article, we studied stationary solutions to the dynamics of a Bose-Einstein condensate corresponding to acoustic (or Unruh) black or white holes, namely, configurations where the flow becomes supersonic, creating a horizon for phonons. In this paper, we consider again the Gross-Pitaevskii equation, but looking for stationary numerical solutions in the case where the couplings are position dependent in a prescribed manner. Initially, we consider a two-dimensional quantum gas in a funnel-like spatial metric. We then reinterpret this solution as a solution in a flat metric but with spatially dependent coupling and external potential. In these solutions, the local speed of sound and the magnitude of flow velocity cross, indicating the existence of a supersonic region and therefore of sonic analogs of black and white holes and wormholes. We discuss the numerical techniques used. We also study phase (and density) fluctuations in these solutions and derive approximate acoustic metric tensors. For certain external potentials, we find uniform-density acoustic-black-hole configurations and obtain their Hawking temperature.
We study acoustic white holes in a steadily flowing atomic Bose–Einstein condensate. A white hole configuration is obtained when the flow velocity goes from a super-sonic value in the upstream region to a sub-sonic one in the downstream region. The scattering of phonon wavepackets on a white hole horizon is numerically studied in terms of the Gross–Pitaevskii equation of mean-field theory: dynamical stability of the acoustic white hole is found, as well as a signature of a nonlinear back-action of the incident phonon wavepacket onto the horizon. The correlation pattern of density fluctuations is numerically studied by means of the truncated-Wigner method, which includes quantum fluctuations. Signatures of the white hole radiation of correlated phonon pairs by the horizon are characterized; analogies and differences with Hawking radiation from acoustic black holes are discussed. In particular, a short wavelength feature is identified in the density correlation function, whose amplitude steadily grows in time since the formation of the horizon. The numerical observations are quantitatively interpreted by means of an analytical Bogoliubov theory of quantum fluctuations for a white hole configuration within the step-like horizon approximation.
We report numerical evidence of Hawking emission of Bogoliubov phonons from a sonic horizon in a flowing one-dimensional atomic Bose–Einstein condensate. The presence of Hawking radiation is revealed from peculiar long-range patterns in the density–density correlation function of the gas. Quantitative agreement between our fully microscopic calculations and the prediction of analog models is obtained in the hydrodynamic limit. New features are predicted and the robustness of the Hawking signal against a finite temperature discussed.
Abstract In this article, we study the dynamics of a Bose–Einstein condensate (BEC) with the idea of finding solutions that could possibly correspond to the so-called acoustic (or Unruh) black/white holes. These are flows with horizons where the speed of the flow changes from sub-sonic to super-sonic. This is because sound cannot return from the supersonic to the subsonic regions. The speed of sound plays the role of the speed of light in a gravitational black hole, with an important difference being that there are excitations that can go faster than the speed of sound and therefore can escape the sonic black hole. Here, the motion of the BEC is described by the Gross–Pitaevskii equation (GPE). More specifically, we discuss singular Stationary solutions of GPE in 2D (with circular symmetry) and 3D (with spherical symmetry). We use these solutions to study the local speed of sound and magnitude of flow velocity of the condensate to determine whether they cross, indicating the potential existence of a sonic analog of a black/white hole. We discuss the numerical techniques used and also study the semi-analytical Laplace–Borel resummation of asymptotic series solutions to see how well they agree with numerical solutions. We also study how the resurgent transseries plays a role in these solutions.
Acoustic analogues of black holes (dumb holes) are generated when a supersonic fluid flow entrains sound waves and forms a trapped region from which sound cannot escape. The surface of no return, the acoustic horizon, is qualitatively very similar to the event horizon of a general relativity black hole. In particular Hawking radiation (a thermal bath of phonons with temperature proportional to the "surface gravity") is expected to occur. In this note we consider quasi-one-dimensional supersonic flow of a Bose–Einstein condensate (BEC) in a Laval nozzle (converging-diverging nozzle), with a view to finding which experimental settings could magnify this effect and provide an observable signal. We discuss constraints and problems for our model and identify the issues that should be addressed in the near future in order to set up an experiment. In particular we identify an experimentally plausible configuration with a Hawking temperature of order 70 n K; to be contrasted with a condensation temperature of the order of 90 n K.
We have created an analog of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. A steplike potential accelerates the flow of the condensate to velocities which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow velocity equals the speed of sound is the sonic event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound. A simulation finds negative energy excitations, by means of Bragg spectroscopy.