Acoustic Black Holes

• Acoustic black holes are analogue gravity systems where supersonic fluid flows form horizons that trap phonons, mirroring key features of gravitational event horizons.
• They are experimentally realized in systems like superfluids, BECs, and classical fluids, allowing direct observation of Hawking-like radiation and entropy dynamics.
• The framework employs effective metric theory, Lorentz violation, and holographic duality to explore quantum chaos, thermodynamics, and information flow in laboratory settings.

Acoustic black holes are analogue gravity systems in which linearized excitations of a medium propagate according to metrics mathematically equivalent to those found in general relativity, admitting causal horizons where information (phonons, sound waves) can no longer escape. The core mechanism involves supersonic flow: when the background fluid velocity locally exceeds the sound speed, an acoustic horizon forms, leading to the trapping of phonons and the emergence of Hawking-like radiation and thermodynamic behavior. Rigorous models map fluid variables such as density, velocity, and sound speed onto effective spacetime metrics, and the dynamics of acoustic horizons recapitulate several phenomena—including Hawking radiation, entropy area laws, geodesic chaos, and lensing—originally predicted for gravitational black holes. Experimental realizations span superfluids, Bose–Einstein condensates, classical fluids, nanostructures, and even engineered mechanical waveguides.

1. Geometric Foundations and Effective Metrics

The propagation of sound waves or equivalent linear disturbances in a moving, barotropic, irrotational fluid is governed by a covariant Klein–Gordon equation in an emergent acoustic metric $g_{\mu\nu}$, constructed from the underlying density $\rho$, flow four–velocity $v_\mu$, and local sound speed $c_s$. In inertial flat spacetime, the general relativistic form is

$$g_{\mu\nu} = \eta_{\mu\nu} + (c_s^2 - 1)\, v_\mu v_\nu$$

where $\eta_{\mu\nu}$ is the background Minkowski metric, and $v_\mu$ satisfies normalization $\eta^{\mu\nu}v_\mu v_\nu=1$ (Mannarelli et al., 2021). For static, spherically symmetric inflows, the metric induces horizon structure at the locus $v^2(r_H) = c_s^2$, where the $g_{tt}$ component changes sign. The acoustic metric fully determines causal propagation for linearly perturbed fields, with horizons acting as one-way membranes for phonons (Wang et al., 2019, Ge et al., 2010, Qiao et al., 2021).

2. Acoustic Horizons, Hawking Radiation, and Entropy Balance

Whenever a stationary flow transitions from subsonic to supersonic, an acoustic horizon is formed: upstream excitations can no longer return to the subsonic region, leading to the irretrievable loss of causal contact. Quantizing the phonon field on this background, one finds spontaneous emission of phonons with a thermal spectrum at a temperature given by the surface gravity. The canonical Hawking temperature is

$$T_H = \frac{1}{2\pi} \left[ \frac{(c_s - |v|)}{(1-c_s|v|)} \right]^{\prime}_{r_H}$$

which, in the nonrelativistic limit, simplifies to $$T_H = \frac{1}{2\pi} \left. \partial_r \left(v-c_s\right) \right|_{r_H}$$, matching the classical sonic-point prediction (Mannarelli et al., 2021).

From the perspective of local entropy balance, the area law is postulated for acoustic horizon entropy: $S_H = \frac{A}{4 L_c^2}$ with $A=4\pi r_H^2$ and $L_c$ the microscopic cutoff. The entropy lost by decreasing the horizon area is exactly compensated by the entropy gain in the radiated phonon gas, permitting a strictly thermodynamic derivation of $T_H$ without recourse to Bogoliubov transformations or explicit tunneling amplitudes (Mannarelli et al., 2021). This framework applies to both equilibrium and non-equilibrium analogues and mirrors quantum-gravitational calculations in general relativity.

3. Classical and Quantum Dynamics Outside Horizons

The geometry outside acoustic black holes closely mimics those of their gravitational counterparts. In the 2+1D draining vortex model, the metric becomes

$$ds^2 = - \left(1 - \frac{\lambda^2}{r^2}\right) dt^2 + \left(1 - \frac{\lambda^2}{r^2}\right)^{-1} dr^2 + r^2 d\phi^2$$

with horizon at $r_H = \lambda$ and Hawking-like temperature $T = 1/(2\pi\lambda)$ (Wang et al., 2019). The dynamics of test vortices (unit-mass particles) admit unstable circular orbits analogous to the photon sphere, with Lyapunov exponents saturating the chaos bound $\Lambda_{\rm Lyapunov} = 2\pi T_H$. Radial infall and sound ray trajectories exhibit lensing, Shapiro-like time delays ($\propto \lambda^2 / r$), and scattering phenomena directly analogous to those in general relativity (Wang et al., 2019). In curved background flows, such as acoustic Schwarzschild analogs,

$$ds^2_{\rm acoustic} = -f(r) dt^2 + f(r)^{-1} dr^2 + r^2 (d\theta^2 + \sin^2\theta d\phi^2)$$

with $f(r)$ incorporating a tuning parameter $\xi$, one observes enhanced bending angles and Einstein ring radii, facilitating direct analog experiments in fluids and BECs (Qiao et al., 2021).

4. Extensions: Lorentz Violation, Noncommutativity, Holography, and Laboratory Realizations

Lorentz Symmetry Breaking: By introducing Lorentz-violating parameters into the Abelian Higgs model, the acoustic metric and Hawking temperature are modified, either by a rescaling of the sound speed or by inducing birefringence, with the general metric form acquiring nontrivial $k_{\mu\nu}$ dependence. Rotating metrics also see changes in the angular velocity and broadening of superresonant amplification bands (Anacleto et al., 2010, Anacleto et al., 2023).

Noncommutative Backgrounds: Quantum-geometry-inspired modifications to the dispersion relation (MDR) and generalized uncertainty principle (GUP) regularize the Hawking temperature and yield characteristic logarithmic corrections to the acoustic entropy,

$S = \frac{A}{4 c_s^2} + \text{(subleading)} \ln A$

predicting the appearance of stable remnants at small horizon radii (Anacleto et al., 2023).

Holographic Duality: In fluids on cutoff surfaces in AdS$_{d+1}$ or D3-brane backgrounds, the formation of an acoustic black hole is the precise holographic dual to fluctuations of the bulk metric. The Hawking-like temperature of the acoustic horizon is universally related to the genuine Hawking temperature of the bulk black brane, and scattering phonons map directly onto sound-channel quasinormal modes of the bulk (Ge et al., 2015, Sun et al., 2017).

Experimental Systems: Acoustic black hole analogues are realized in:

• Classical fluids: draining bathtubs, water tanks, spiral vortices (Lemos, 2013, Ge et al., 2010).
• Bose–Einstein condensates: Gross–Pitaevskii theory maps directly onto relativistic acoustic metrics, with horizons engineered by radial flow profiles or traps (Coviello et al., 30 Sep 2024, Santos et al., 25 Jun 2025).
• Superconductors: Josephson junctions exploit phase gradients and magnetic fields to achieve supersonic flow and measurable Hawking temperatures on the order of $10^{-7}$ K (Ge et al., 2010).
• Electron flows: Hydrodynamic electron fluids produce observable current-noise signatures of acoustic Hawking radiation, with cross-correlations indicative of entangled phonon emission (Dave et al., 2022).
• Mechanical waveguides: Asymmetric power-law tapers in beams induce one-way trapping of flexural waves, with reflectionless behavior across broad frequency bands optimized via geometry and damping coatings (Soroor et al., 1 Nov 2025).

5. Thermodynamic Laws, Entropy, and Information-Theoretic Aspects

Two-dimensional acoustic black holes admit a precise thermodynamic interpretation: the first law,

$dE = T_H dS$

with the entropy universally proportional to the integral of density at the horizon. In analogue gravity systems, Page curves for entanglement entropy of radiated phonons are explicitly calculated using the island prescription, reproducing the unitarity-restoring plateau and linking late-time entropy to the area of the acoustic horizon. In extremal limits (vanishing surface gravity), entanglement entropy diverges, leading to ill-defined Page times (Zhang, 2016, Cheng et al., 10 Dec 2025).

The Page curve and island construction are mirrored in both equilibrium and non-equilibrium regimes, revealing deep correspondence between entropic flows and causal structures in both gravitational and acoustic black holes.

6. Ringdown, Instabilities, Clouds, and Quantum Chaos

Acoustic black holes exhibit quasinormal ringing, power-law late-time tails, and superresonance, paralleling Kerr black hole physics. Rotating draining bathtub analogues reveal superresonant amplification ($\omega < m\Omega_H$), sonic bombs, and stable acoustic clouds confined by mirrors with discrete spectrum determined by synchronization conditions $\omega = m\Omega_H$. The entire spectrum—including greybody factors and transmission coefficients—is accessible via analytic confluent Heun function solutions to the massless Klein–Gordon equation (Lemos, 2013, Vieira et al., 2014, Benone et al., 2014).

Chaotic dynamics are quantified via Lyapunov exponents for perturbed orbits near the acoustic horizon; in non-extremal cases, the Maldacena-Shenker-Stanford bound $\lambda \leq 2\pi T_H$ is satisfied, while in extremal configurations the bound is violated due to vanishing surface gravity (Singh et al., 20 May 2024, Wang et al., 2019).

7. Comparison to Gravitational Black Holes and Outlook

Acoustic black holes replicate not just the kinematical features (horizons, lensing, stable/unstable orbits) but also thermodynamic, quantum, and information-theoretic phenomena originally predicted for gravitational black holes. The area law for entropy, universality of Hawking temperature, existence of clouds, quasinormal modes, superresonance, and information paradox all appear in analogue form, accessible in laboratory systems. The robustness of these features across relativistic, non-relativistic, Lorentz-violating, noncommutative, and holographic models underscores the deep connection between geometry, causality, and statistical mechanics in both real and synthetic spacetime backgrounds.

Current and proposed experimental efforts in water waves, BECs, superconductors, and electronic systems continue to probe the full phenomenology of acoustic black holes, providing a fertile platform for testing foundational aspects of black hole physics, quantum chaos, and emergent thermodynamics (Ge et al., 2010, Soroor et al., 1 Nov 2025, Coviello et al., 30 Sep 2024, Dave et al., 2022).