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Acoustic Black Hole in a 1D Bose-Einstein Condensate with a Topological Defect: A Numerical Study

Ruslan Kudinov

Published Jun 19, 2026• 0 citations
Publisher

Abstract

What happens when sound itself cannot escape? In this work, a 1D Bose-Einstein condensate is manipulated with a topological defect — a phase profile with an odd number of half-twists, inspired by the Möbius strip. The result: the speed of sound drops to zero. A region is created where sound waves simply cannot enter — an acoustic event horizon. This is not a black hole in space. But it is the exact analogue of one: a region from which nothing (not even sound) can escape. The simulation is based on the Gross-Pitaevskii equation and solved with a split-step Fourier method. No fitting parameters are used. The code is open source and available on GitHub. If we can create an acoustic horizon in a laboratory, what else can we create? This work explores the boundary between condensed matter physics and general relativity — and suggests that topological defects may be the key to controlling spacetime itself.

DOI
10.5281/zenodo.20765867

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What happens when sound itself cannot escape? In this work, a 1D Bose-Einstein condensate is manipulated with a topological defect — a phase profile with an odd number of half-twists, inspired by the Möbius strip. The result: the speed of sound drops to zero. A region is created where sound waves simply cannot enter — an acoustic event horizon. This is not a black hole in space. But it is the exact analogue of one: a region from which nothing (not even sound) can escape. The simulation is based on the Gross-Pitaevskii equation and solved with a split-step Fourier method. No fitting parameters are used. The code is open source and available on GitHub. If we can create an acoustic horizon in a laboratory, what else can we create? This work explores the boundary between condensed matter physics and general relativity — and suggests that topological defects may be the key to controlling spacetime itself.
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.
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.
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 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.
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.
Based on the one-dimensional Gross-Pitaevskii equation (GPE) model, this work studies the formation of acoustic black holes in one-dimensional Bose Einstein condensate (BEC) in harmonic oscillator external potential, and extending the applicable scenarios of the GPE model for its specific application of simulating the formation conditions of acoustic black holes in one-dimensional systems. At the same time, We deepen the understanding of the analytical formula for determining the production conditions of acoustic black holes and the evolution formula of the radius of acoustic black holes.