Breath of the Abyss: How a Black Hole's Horizon Pulsates to the Rhythm of Accretion ✦

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 · ⏱ 1 min · General Relativity High Energy

Nonlinear accretion turns a black hole’s acoustic horizon into a breathing organ: its radius pulsates in sync with density and temperature fluctuations, opening the door to laboratory analog gravity.

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A black hole's acoustic horizon is not a wall. It's a breathing membrane: nonlinear accretion pulsations shift it by hundreds of millions of kilometers. For the center of the Milky Way, the sound horizon almost merges with the gravitational one, pulsating to the beat of plasma temperature and density. Such breathing is a key to recreating Hawking radiation in earthly labs and a new window into black hole thermodynamics.

🎯 The acoustic horizon of Sgr A* 'breathes' with a swing of hundreds of millions of kilometers—larger than Earth's orbit around the Sun. Its pulsation period, from hours to days, matches the gas crossing time through the inner disk, turning the horizon into a giant cosmic chronometer.

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

The acoustic horizon radius is expressed through the accretion rate f, plasma density ρ, and speed of sound 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 relative change in horizon radius depends on fluctuations in accretion, density, and temperature; the thermodynamic contribution is described by the derivative of the adiabatic index Γ with respect to the dimensionless temperature Θ.

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Breath of the Abyss: How a Black Hole's Horizon Pulsates to the Rhythm of Accretion ✦