Acoustic Black Holes

An acoustic black hole is a transonic fluid background on which small sound perturbations cannot propagate upstream across a sonic horizon. Its importance is exact but limited: under stated hydrodynamic assumptions, the perturbation obeys a massless wave equation in an effective Lorentzian geometry. The background fluid still follows fluid mechanics, not Einstein’s equations.

Acoustic geometry and physical status

Property	Statement
Object class	Analogue system
Medium	Barotropic, inviscid fluid; irrotational background for the standard scalar derivation
Propagating field	Linear velocity-potential perturbation
Horizon	Normal background velocity equals the low-frequency sound speed
Controlled regime	Wavelengths long compared with the microscopic or dispersive scale
Physical status	Laboratory and theoretical kinematic analogue; not a gravitational black hole

Let the background density, velocity, and sound speed be $\rho_0$, $\mathbf v_0$, and $c_s^2=dp/d\rho$. Linearize continuity and Euler equations about a background that itself solves those equations, and write $\mathbf v=\nabla\Phi$. The perturbation $\phi_1=\delta\Phi$ satisfies

$$\frac{1}{\sqrt{-g_{\rm ac}}} \partial_\mu\!\left(\sqrt{-g_{\rm ac}}\, g_{\rm ac}^{\mu\nu}\partial_\nu\phi_1\right)=0,$$

with representative acoustic line element

$$ds_{\rm ac}^2=\frac{\rho_0}{c_s} \left[-(c_s^2-v_0^2)dt^2 -2v_{0i}\,dt\,dx^i+\delta_{ij}dx^i dx^j\right].$$

Unruh 1981, complete short article, pp. 1351–1353 identified this causal structure, and Visser 1998, §§2–4 established the general acoustic-geometry formulation. The conformal factor does not change sound rays, but it matters for the full wave operator and therefore cannot always be discarded.

Horizon scale and controlled checks

For a stationary surface with outward unit normal $\mathbf n$, a sonic horizon occurs where the normal component obeys $v_\perp=\mathbf v_0\!\cdot\!\mathbf n=-c_s$ for an inward flow. A commonly used gradient scale is

$$\kappa_{\rm ac} =\left.\frac{1}{2c_s}\, \partial_n\!\left(c_s^2-v_\perp^2\right)\right|_H ,$$

after fixing laboratory time and orientation. The kinematic temperature parameter is $T_{\rm ac}=\kappa_{\rm ac}/(2\pi)$. It characterizes low-frequency Bogoliubov ratios under near-stationary, adiabatic conditions; it is not a thermodynamic temperature derived from a gravitational first law. The distinction is developed in Surface Gravity and Hawking Temperature.

Three checks delimit the construction. With $\mathbf v_0=0$ and constant $\rho_0,c_s$, the equation reduces to the ordinary sound wave equation. When the normal flow never reaches $c_s$, there is no acoustic blocking horizon even if the medium is inhomogeneous. Finally, as wavelength approaches the medium scale, the linear dispersion becomes

$$(\omega-\mathbf v_0\!\cdot\!\mathbf k)^2 =c_s^2k^2\,[1+O(k^2\xi^2)],$$

so the metric description must be replaced by the measured dispersive theory. Recovery of the nondispersive result as $k\xi\to0$ is a required limit.

Mode conversion and strongest result

The conserved inner product of the linearized action assigns opposite norm to branches with opposite comoving frequency. Scattering at a stationary horizon can therefore mix positive- and negative-norm modes. Upon quantization, the outgoing operator has the form

$$\hat a_{\rm out} =\alpha_\omega\hat a_{\rm in} +\beta_\omega\hat b_{\rm in}^{\dagger}, \qquad |\alpha_\omega|^2-|\beta_\omega|^2=1.$$

The strongest established result is the derivation and repeated laboratory realization of this kinematic scattering structure. Under smooth backgrounds and suitable separation between $\kappa_{\rm ac}$ and the dispersive scale, low-frequency conversion can be robust against ultraviolet modifications; Unruh and Schützhold 2005, §§III–VII state the assumptions behind that universality. Near-Horizon Universality of the Hawking Effect gives the gravitational calculation to which it is compared.

Stimulated conversion tests $\alpha_\omega$ and $\beta_\omega$ with a prepared classical input. Spontaneous emission requires a quantum state close to the incoming quasiparticle vacuum and an observable that distinguishes created pairs from technical noise. A thermal output spectrum alone does not do so.

Dynamics, measurement, and inference systematics

The background and perturbation timescales must be separated. Let $\tau_{\rm bg}$ characterize drift of the velocity profile and $\tau_{\rm sc}$ the wave-packet crossing time. A stationary scattering interpretation requires $\tau_{\rm bg}\gg\tau_{\rm sc}$; otherwise frequency is not conserved and ordinary parametric production joins horizon conversion. The incident state should be measured upstream in the same mode basis used for the output, rather than inferred from a nominal drive setting.

Platform observables differ. Microphones or pressure sensors measure a filtered classical field; particle-image velocimetry reconstructs the flow; quantum fluids can access density covariances. In every case, converting a sensor spectrum into $|\beta_\omega|^2$ requires the mode functions, group velocities, norm factors, and transfer function. A flux check should sum every open outgoing branch. An apparent deficit may be dissipation, leakage into transverse or vortical modes, or an incomplete scattering basis—not pair creation.

The resulting inference systematics include uncertainty in the reconstructed background, leakage between mode windows, finite record length, calibration drift, and the prior used for unobserved branches. They must accompany any quoted temperature or occupation rather than being folded into an unexplained fit residual.

Principal obstruction and evidence boundary

Real fluids are viscous, dispersive, finite, and often vortical. Background gradients can couple sound to entropy or transverse modes; dissipation makes the norm balance nonunitary; an abrupt horizon preparation generates unrelated excitations. Reliable inference therefore needs independent measurements of $\rho_0$, $\mathbf v_0$, $c_s$, dispersion, attenuation, input covariance, detector response, and stationarity.

At the 20 August 2026 evidence cutoff, acoustic platforms strongly establish effective metrics and horizon mode conversion, with quantum claims depending on the particular medium and state diagnostic; Barceló, Liberati, and Visser 2026, §§2, 5.1, 6–7.1 review the full construction and experimental landscape. The principal conceptual obstruction is unchanged: the effective metric has no analogue Einstein equation. The fluid’s density and velocity are not determined by acoustic curvature, phonon backreaction is medium-specific, and no area entropy follows. Acoustic evidence supports a wave-mechanical mechanism, not semiclassical gravity.

References

• Barceló, Carlos, Stefano Liberati, and Matt Visser. “Analogue Gravity.” Living Reviews in Relativity 29 (2026), article 2. doi:10.1007/s41114-026-00064-9.
• Unruh, William G. “Experimental Black-Hole Evaporation?” Physical Review Letters 46 (1981), 1351–1353. doi:10.1103/PhysRevLett.46.1351.
• Unruh, William G., and Ralf Schützhold. “Universality of the Hawking Effect.” Physical Review D 71 (2005), 024028. doi:10.1103/PhysRevD.71.024028.
• Visser, Matt. “Acoustic Black Holes: Horizons, Ergospheres and Hawking Radiation.” Classical and Quantum Gravity 15 (1998), 1767–1791. doi:10.1088/0264-9381/15/6/024.