Analog Gravity: How the Whisper of Accretion Turns into the Roar of Nonlinear Horizons ✦

Original: "Emergent gravity from nonlinear perturbation of spherical accretion with variable adiabatic index"

· Rohit Ghosh, Souvik Ghose, Biplab Raychaudhuri, Apashanka Das, Tapas K. Das

arXiv:2605.04158v2 · 2026-05-05 · CC BY 4.0 · ⏱ 3 min · General Relativity High Energy

Nonlinear perturbations in the accreting flow around a black hole give rise to a dynamic acoustic spacetime, where the horizon shifts in rhythm with density and temperature pulsations.

Abstract

The aim of the work is to show that analogue gravity phenomena are not limited to linear perturbations but also arise in the nonlinear analysis of supersonic flows. Spherical accretion onto compact objects is considered with a relativistic multicomponent equation of state and variable adiabatic index. The acoustic metric formalism is extended beyond the linear approximation: it is shown that perturbations satisfy a covariant wave equation in an effective acoustic spacetime with nonlinear corrections that make the geometry dynamic. As a result, the acoustic horizon can shift inward or outward depending on the amplitudes of density, temperature, and accretion rate fluctuations. This provides a more realistic basis for investigating the dynamics of nonlinear analogue spacetime in astrophysically significant accretion flows.

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Context

Imagine a river speeding up and becoming supersonic—sound born downstream can no longer travel back against the raging current. This simple analogy underpins the concept of an analogue black hole, where sound, rather than light, is trapped. On astrophysical scales, such effects arise when interstellar gas accretes onto compact objects like black holes or neutron stars. These flows naturally become supersonic, spawning acoustic horizons—surfaces from which sound cannot escape. Studying these horizons opens a window into the physics of real black holes, allowing us to test Hawking's predictions about radiation and the quantum nature of gravity.

Methods

To move beyond simplified models, the authors considered a plasma of electrons, positrons, and protons with a relativistic equation of state where the adiabatic index changes with temperature. A second-order nonlinear perturbation method was analytically developed for the accretion rate and density. The resulting wave equation sees higher-order corrections turn the static acoustic metric into a dynamic one—much like ripples on water alter the 'horizon' seen by a swimmer. A Newtonian potential was used in the calculations, with the speed of light set to unity; metric components were expressed through background and perturbed quantities.

Results

The key result: nonlinear perturbations make the acoustic spacetime evolve. The sonic horizon no longer sits still—it shifts inward or outward depending on the balance of density, temperature, and accretion rate fluctuations. For a steady background modeled on the supermassive black hole at the Galactic Center (Sgr A*), the radius of the acoustic horizon turned out to be 2.131 Schwarzschild radii (Schwarzschild), and the ion plasma temperature at the horizon was about 9·10^11 K, consistent with Event Horizon Telescope observations. Linear perturbations, both standing (for neutron stars) and traveling (for black holes), proved stable—oscillations do not grow, meaning the acoustic 'echo' does not disrupt the structure.

Implications

Thus, analogue gravity is not an artifact of weak perturbations but a property that emerges even in strong nonlinear regimes. This brings laboratory and numerical models closer to real accreting objects, where turbulence and shock waves are inevitable. The results are important for interpreting data from the Event Horizon Telescope and future X-ray observatories.

Future development

The next step is to include rotation, magnetic fields, and a full general-relativistic description. It will be interesting to see how nonlinearities affect predictions of 'quantum evaporation' of acoustic horizons, akin to Hawking radiation. Perhaps dynamic horizons will produce non-stationary phonon streams, opening new parallels with the thermodynamics of black holes.

Impact

The study will influence accretion astrophysics, plasma physics, and experiments on analogue gravity in Bose-Einstein condensates.

Next steps

In the immediate plans: simulations with axial symmetry and magnetohydrodynamics, plus comparison with observed spectra of quasi-periodic oscillations in X-ray binaries.

Key open problems

The work touches on the problem of the black hole horizon as a 'hologram'—if the acoustic horizon behaves so plastically, might the same hold for real horizons in quantum gravity? It is also indirectly related to the information paradox and the nature of singularities.

🎯 Did you know that for the supermassive black hole at the center of the Milky Way, the acoustic horizon lies just 6% farther out than the gravitational one? This means the point where plasma stops 'hearing' its outer part nearly coincides with the surface from which light cannot return.

c_s^2 = \frac{2\Gamma\Theta}{\alpha}

Here \(\Gamma\) is the adiabatic index, \(\Theta\) is the dimensionless temperature, and \(\alpha\) is a composition parameter of the medium.

r_H^4 = \frac{f^2}{\rho^2 c_s^2}

The horizon radius \(r_H\) is determined by the accretion rate \(f\), density \(\rho\), and sound speed \(c_s\).

\frac{\delta r_H}{r_H} = \frac{1}{2}\left[ \frac{\delta f}{f} - \frac{\delta \rho}{\rho} - \frac{1}{2}\left(\frac{1}{\Theta} + \frac{1}{\Gamma}\frac{d\Gamma}{d\Theta}\right)\delta\Theta \right]

The change in radius depends on fluctuations in the accretion rate, density, and temperature.

Key numbers

mass accretion rate (f0): 2.199
acoustic horizon radius (r_H): 2.131 GM/c²
dimensionless temperature at horizon (Θ_H): 152.263
plasma temperature at horizon for Sgr A*: ~9·10¹¹ K
horizon radius for Sgr A*: ~1.357·10¹⁰ m

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