Static Acoustic Black Holes: Theory & Applications

• Static acoustic black holes are stationary configurations in compressible media where fluid velocity equals local sound speed, forming a sonic horizon analogous to gravitational black holes.
• They are realized across diverse systems such as Bose–Einstein condensates, machined flexural structures, and superconducting junctions via analytic and numerical hydrodynamic mappings.
• Their study reveals rich phenomena including tunable Hawking-like temperatures, distinct wave scattering, and spin-dependent tidal Love numbers, challenging traditional GR no-hair theorems.

A static acoustic black hole (ABH) is a stationary spacetime geometry, realized in a compressible medium, wherein the local flow speed surpasses the speed of sound within a finite region, thereby creating a sonic event horizon analogous to the causal boundary of a gravitational black hole. ABHs are defined by static backgrounds, as opposed to evolving or rotating (“Kerr-like”) flows, and encode rich phenomenology in both their macroscopic wave dynamics (metric structure, horizon thermodynamics) and their response to external perturbations (tidal Love numbers, quasibound states). ABHs arise in a wide variety of physical systems including classical fluids, Bose–Einstein condensates, engineered phononic structures, superconductor junctions, hydrodynamic models with modified inertia, and gauge-theoretic settings with broken Lorentz invariance.

1. Fundamental Concepts and Metric Structure

The defining feature of a static ABH is the existence of a stationary transonic flow, so the normal component of the medium velocity $v$ equals the local sound speed $c_s$ at a finite horizon radius $r_h$:

$|v(r_h)| = c_s(r_h).$

The effective acoustic metric for perturbations (e.g. phonons, scalar fields) is generically of Unruh type:

$$ds^2 = -[c_s^2 - v^2(r)]\,dt^2 - 2v(r)\,dt\,dr + dr^2 + r^2 d\Omega^2,$$

where $d\Omega^2$ encodes the angular part for $(2+1)$ or $(3+1)$ dimensions. For ABHs realized in fluids described by neo-Newtonian hydrodynamics, the pressure $p$ enters via the inertial factor, replacing the density prefactor with $\rho_0 + p_0/c^2$ and modifying horizon formation conditions (Fabris et al., 2013).

In engineered media and Bose–Einstein condensates, the local metric structure is obtained by mapping the background to a stationary solution of the Gross–Pitaevskii equation and reading off $v(r)$ and $c_s(r)$ from the phase and density profiles, with sonic horizons appearing where the flow crosses the sound speed (Vaidya et al., 2024, Vaidya et al., 2024). In Josephson junctions, the metric takes the form:

$$ds^2 = \frac{\hbar\rho_0}{mc_s} \left[ - (c_s^2 - v_0^2)\,dt^2 - 2v_0\,dt\,dx + dx^2 \right]$$

with tunable parameters via barrier thickness and supercurrent density (Ge et al., 2010).

2. Formation, Realization, and Analytical Construction

Static ABHs are constructed by setting up stationary solutions of the governing hydrodynamic, quantum, or solid-state field equations. In Newtonian and neo-Newtonian fluids, analytic solutions with irrotational, spherically symmetric flow produce horizons when the radial velocity reaches $c_s$ at some $r_h$, with pressure effects shifting $r_h$ and $T_H$ (Fabris et al., 2013). In Bose–Einstein condensates (BECs), stationary ABH profiles are obtained by solving the time-independent GPE for $$\Psi(r,t) = \sqrt{n(r)}\, e^{i\phi(r)-i\mu t/\hbar}$$ subject to boundary conditions (subsonic at infinity, horizon at finite $r_h$) (Vaidya et al., 2024, Vaidya et al., 2024). Singular flow solutions are confirmed by Chebyshev–Newton collocation, BVP+IVP numerical integration, and Laplace–Borel resummation of asymptotic series.

In solid-state and structural engineering, ABHs are realized via spatially-varying cross-section or mass profiles—most notably, power-law tapers in beams or plates—whose gradual impedance gradient traps bending or flexural waves, effectively creating an analog horizon for broadband acoustic energy (Soroor et al., 1 Nov 2025, Zhu et al., 2014, Sampath et al., 2021). In quantum gauge models with Lorentz violation, the effective ABH metric follows from the linearization of the Abelian–Higgs field equations with an explicit breaking tensor $k^{\mu\nu}$, producing anisotropic cones and distinct Hawking temperatures for each phonon species (Anacleto et al., 2010).

3. Wave Dynamics, Quasibound States, and Love Numbers

Linear perturbations of ABH backgrounds obey static master equations, typically reducible to hypergeometric (or in Schwarzschild ABH, Heun-type) ODEs for the radial profile of the field. Quasibound state spectra are analytically calculable for Schwarzschild ABHs, yielding purely imaginary, overdamped frequency modes, and exhibit stronger decay (damping) than their general-relativistic Schwarzschild analogs (Vieira et al., 2021). The ABH response to external tidal fields is captured by dimensionless static Love numbers, defined as the amplitude ratio of decaying (“response”) to growing (“source”) field modes at large $r$:

$F_{\ell m} = \frac{\alpha}{\beta}.$

In $(3+1)$ dimensions, scalar (bosonic) ABHs generically possess nonzero $F^{(s=0)}_{\ell m}$ (except for $\ell$ a multiple of $4$), whereas fermionic ABHs (Dirac/Weyl fields) show universal power-law $F^{(s=±1/2)}_{\ell m} = \pm 4^{-(\ell+1/2)}$ (Du et al., 29 Dec 2025). In $(2+1)$ dimensions, scalar Love numbers vanish for even $m$ (due to a logarithmic expansion structure) but are nontrivial for odd $m$; fermionic cases retain $F_m = 4^{-m}$, always nonzero. This marks a major distinction from GR Schwarzschild metrics, for which all bosonic static Love numbers vanish (Du et al., 29 Dec 2025).

4. Thermodynamics, Horizon Entropy, and Hawking-like Emission

The Hawking temperature $T_H$ of a static ABH is set by the surface gravity at the horizon:

$$T_H = \frac{\hbar}{2\pi k_B} \left. \frac{1}{2} \frac{d}{dr}(c_s^2 - v^2(r)) \right|_{r_h},$$

with detailed formulae depending on the particular realization and the inclusion of relativistic corrections or Lorentz-violation (Fabris et al., 2013, Anacleto et al., 2010). The phonon emission spectrum at the horizon is thermal:

$f(\omega) = \frac{1}{e^{\omega/T_H} - 1},$

and the horizon entropy satisfies an area law:

$S_H = \frac{A}{4L_c^2},$

where $L_c$ is a system-specific cutoff (analogous to Planck length in gravity) (Mannarelli et al., 2021). The entropy loss of the ABH is balanced by the entropy gain of the emitted phonon gas, confirming the robustness of the thermodynamic analogy. In structured media and quantum fluids, numerical and analytic methods confirm the Euclidean regularity condition and support the existence of well-defined ABH Hawking temperatures across implementations (Vaidya et al., 2024, Vaidya et al., 2024, Anacleto et al., 2010).

5. Experimental Realizations and Applications

Static ABHs have been engineered and experimentally validated in numerous platforms:

• BEC flows: ABH horizons and singularities are mapped via stationary GPE solutions, with numerical agreement achieved by resurgent transseries and PINN methods, providing a laboratory setting for analog Hawking radiation studies (Vaidya et al., 2024, Vaidya et al., 2024).
• Machined flexural structures: Power-law tapers in beams and plates yield broadband wave absorption with minimal reflection. Optimal taper exponents ($m \approx 3$), loss-factor-dampened layers, and structural mappings onto complex geometries (airfoils, lattices) produce strong traveling-wave mitigation and spatial/frequency-selective modulation of vibrational energy (Soroor et al., 1 Nov 2025, Zhu et al., 2014, Sampath et al., 2021).
• Superconducting junctions: Josephson devices with controllable tunneling currents and field-induced flow profiles permit explicit tuning of $T_H$ to observable cryogenic ranges, bridging quantum electronics with analog gravity (Ge et al., 2010).
• Gauge-theoretic and holographic fluids: ABHs in Abelian–Higgs models and AdS brane setups provide direct connections between analog horizon physics and broader theoretical constructs, including Lorentz violation and fluid/gravity correspondence. Notably, the mapping between phonon quasinormal modes and sound-channel QNMs in AdS backgrounds establishes a duality between laboratory ABHs and true gravitational black holes (Ge et al., 2015, Anacleto et al., 2010).

6. Theoretical Implications and Distinctions

Static ABHs expand the analog gravity paradigm by incorporating the fundamental response difference between bosonic and fermionic degrees of freedom. While bosonic ABHs manifest generically nonzero love numbers and tidal deformation responses—admitting laboratory observables absent in GR—fermionic responses follow a universal, background-independent power law (Du et al., 29 Dec 2025). The presence of horizons, real or step-like, leads to rich scattering matrices with Hawking pair creation interpreted via negative-norm channels and evanescent mode interference (Curtis et al., 2018).

Differences with gravitational black holes include the accessibility of internal regions (lack of strict causal isolation due to superluminal excitations in some models), the sensitivity of horizon formation to background pressure and fluid equation of state (Fabris et al., 2013), and the presence of Lorentz violation effects in phonon spectrum and Hawking emission (Anacleto et al., 2010). ABHs in structured media produce distinctive dispersion phenomena such as zero group velocity points, negative refraction, bi-refraction, and anisotropy (Zhu et al., 2014).

A plausible implication is that ABHs, due to their non-rigid, compressible medium basis, can host measurable tidal response and evade the strict “no hair” theorems of general relativity, while simultaneously encoding deeper symmetry features in their spin-dependent response.

7. Outlook and Open Problems

Research continues on dynamical formation, quantum fluctuation phenomena (Hawking radiation, information paradox analogs), more realistic modeling including dissipation and nonlinearity, extension to higher-dimensional and nontrivial topologies, and experimental observation of spin-dependent Love numbers. The role of evanescent modes in information leakage, their impact on the restoration of unitarity, and the use of static ABHs for quantum simulation and signal processing in solid-state environments remain vibrant open questions (Curtis et al., 2018, Vaidya et al., 2024, Du et al., 29 Dec 2025). ABHs thus offer a unique, experimentally accessible framework for probing fundamental properties of horizon physics, quantum field response in curved spacetime, and the spin structure of tidal deformation phenomena.