Cosmic Fountain: How Shock Waves Control the Growth of Black Holes ✦
For the first time, researchers have built a complete picture of shock waves arising when a gas cloud collapses into a black hole, accounting for relativistic effects. The jump conditions allowed linking the infalling inner matter to an outer shell, which can be stationary, expanding, or contracting. A rich family of solutions was discovered: shock waves can accelerate up to 40% of the speed of light (about 120,000 km/s), and the accretion rate drops by a factor of 5–7 compared to smooth compression. The energy released at the shock front reaches 10% of the rest mass—nearly twice as efficient as standard accretion. This explains the rapid growth of supermassive black holes in the early universe and the nature of recently discovered 'little red dots.'
Observations by James Webb showed: already 500 million years after the Big Bang (at redshifts z~10), the Universe was aglow with black holes with masses of billions of solar masses. This baffles theories of gradual growth: matter would not have time to 'feed' the seeds at the required rate. One likely way out is direct collapse of low-metallicity gas into a massive object. However, until now there was no precise picture of such a collapse. Classical models painted a smooth, unimpeded fall.
But the laws of thermodynamics demand otherwise. The growth of entropy during compression inevitably gives birth to a discontinuity — a relativistic shock wave. It is this wave, like a frenzied cosmic fountain, that stands in the path of the collapsing gas. In a new work, physicists found exact self-similar solutions of the equations of general relativity of Einstein for such a wave in an isothermal sphere. Using the Schwarzschild metric and generalizing the Landau–Lifshitz conditions to the relativistic case, they showed: the front speed reaches ~40% of the speed of light, and the ejected energy — up to 10% of the rest mass of the infalling matter. For comparison: thermonuclear fusion in stars converts only 0.7% of mass into radiation. Here gravity squeezes almost 15 times more — efficiency comparable to annihilation of matter and antimatter.
Such dynamics paint a different portrait of a growing black hole. The central accretion rate drops by 5–7 times compared to the shock-free scenario: while matter is fountain-ing, it barely adds mass. This mechanism serves as a powerful feedback — a natural growth regulator. Moreover, the colossal energy release (~10⁵⁷–10⁵⁸ erg) heats and inflates the circum-black-hole shell, turning newborn objects into the mysterious 'red dots' — compact active galactic nuclei in dusty cocoons, which is what JWST observes.
Generalization to rotation and magnetic fields, going beyond the isothermal approximation — are the next steps. It is already clear: such shock-wave fountains could have served as a trigger for quasars in the young Universe, and their gravitational-wave echo might be caught by future detectors. Numerical simulation will verify the realism of this analytical scenario and turn it into a working tool for reading the history of the cosmos.
🎯 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.