Cosmic Fountain: How Shock Waves Control the Growth of Black Holes ✦

Original: "General Relativistic Shock Wave Solutions with Black Hole Formation: The Singular Isothermal Sphere Case"

· Chien-Ting J. Chen, Michael J. Cai, Fabio Pacucci

arXiv:2606.29607 · 2026-06-28 · CC BY 4.0 · 1 min · High Energy Cosmology Galaxies General Relativity

Shock waves during gravitational collapse of isothermal gas turn the birth of a black hole into a cosmic fountain: ejecting up to 10% of rest energy, they regulate accretion and explain the rapid growth of supermassive black holes in the early Universe.

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Already 500 million years after the Big Bang, black holes of a billion suns exist — many times faster than old models allowed. The key is a shock wave acting like a cosmic fountain: it ejects gas, slowing accretion by 5–7 times, and converts up to 10% of mass into radiation (compare with 0.7% for thermonuclear fusion). Such explosions could have ignited the first quasars and explain JWST's red dots.

🎯 In shock-wave solutions, gas doesn't just fall into the black hole, but performs a 'fountain' loop: first the shock wave flings it outward, and only when the expanding zero-velocity surface catches up with the gas, it turns around and rushes unimpeded toward the singularity.

p_{\rm pre} p_{\rm post} = \frac{\gamma}{1+\gamma}

The product of the proper momenta of the gas before and after the shock front is constant and depends only on the square of the sound speed.

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Cosmic Fountain: How Shock Waves Control the Growth of Black Holes ✦