A Black Hole’s Sound Horizon Pulses with Infalling Gas ✛ ✦

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

Around a black hole, infalling gas turns into a supersonic flow, and its violent swirls make the sound horizon waver.

When a crowd rushes into a stadium, screams get lost in the roar of the crush — sound can't escape. That's exactly how gas behaves as it falls towards a black hole: accelerating to supersonic speeds, it creates a boundary from which sound can no longer emerge. This sound horizon is an analogue of the boundary beyond which even light cannot escape.

But unlike a simple picture, the flow of interstellar gas isn't smooth — it churns with turbulence, like a crowd where people press unevenly. These surges in the plasma of the spinning disk make the sound barrier 'breathe': it shifts with every jump in density and temperature. For the supermassive black hole at the center of the Milky Way, the radius of this horizon lies just beyond twice the Schwarzschild radius (the boundary from which light can't escape) — and this edge pulsates.

What's most striking is that for the galactic center, the sound horizon sits just 6% farther out than the gravitational one. The point from which neither light nor sound escapes is almost the same.

Such models turn guesswork into calculations. For neutron stars and black holes in curved spacetime, these pulsations might hint at how to test Hawking's idea of quantum radiation. And the origins lie in work on stellar mass limits, including the Chandrasekhar limit.

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For the supermassive black hole at the Milky Way's center, the sound horizon is only 6% farther out than the gravitational one — nearly the same place from which light can't escape.

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.

Scientists

Stephen Hawking Jacob Bekenstein Fritz Zwicky Karl Schwarzschild Subrahmanyan Chandrasekhar Rainer Weiss

Concepts

teleparallel gravity entropic gravity geodesic equation spacetime curvature Archimedes' principle spacetime emergence gravitational perturbation gravitational wave propagation entropic shadow Accretion disk anomalous hall effect ergodic theorem nonadiabatic transition general relativity tidal charge accretion disk wind negative pressure analog black hole arrow of time self interaction

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A Black Hole’s Sound Horizon Pulses with Infalling Gas ✛ ✦