How Pressure Stops Black Holes from Being Born express

Original: "Saturation Equations of State in Critical Gravitational Collapse: The Primordial Black Hole Threshold"
· Benaoumeur Bakhti
arXiv:2606.29590 · 2026-06-28 · CC BY 4.0 · 2 min
The pressure of matter can raise the threshold at which a clump of material collapses into a primordial black hole.

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In the first moments after the Big Bang, the universe was filled with a hot, nearly uniform plasma. But in some places, the density could randomly be slightly higher. If such a clump gained critical mass, it collapsed into a black hole: this is how primordial black holes were born.

For a long time, theorists assumed that matter under those conditions behaved like radiation: pressure grew strictly proportional to density. But what if, under extreme compression, matter starts to 'stiffen'—its pressure skyrockets much faster? The authors of the study tested this idea using a simple model: they replaced radiation with a 'lattice gas'—a system where particles cannot occupy the same space. When density approaches the limit, sound in such a medium speeds up, and the matter desperately resists further compression.

Pressure in this model grows nonlinearly: at low density it is almost like radiation, but near saturation it sharply stiffens. This resembles a crowd in a subway car: as long as there is free space, everyone stands calmly, but when you can't fit another person, every move meets stiff resistance.

The researchers ran a series of numerical simulations of spherically symmetric collapse within the framework of general relativity. They found that the threshold for black hole formation increased by 0.50±0.02% compared to the case of pure radiation. That's small, but enough to shift predictions about how many primordial black holes might have survived to the present day. Meanwhile, the critical mass exponent remained the same—0.357, within measurement uncertainty. This means the collapse mechanism near the threshold hasn't changed; it just takes a bit more initial density to trigger it.

Primordial black holes are candidates for dark matter. If their formation threshold depends on the properties of matter, then the total mass of such holes in the universe could be different than previously thought. Even half a percent on a cosmic scale can change the picture.

In the densest part of a neutron star, sound can accelerate to nearly the speed of light — about 200,000 km/s.

In Bruce Sterling's novel 'Schismatrix', intelligent beings manipulate ultra-dense matter to build cities on neutron stars.

Scientists
Stephen HawkingJacob BekensteinJohn Archibald WheelerFritz ZwickyKarl SchwarzschildSubrahmanyan Chandrasekhar
Concepts
critical collapse black hole mass equation of state black hole memory burden nuclear reaction mass gap barrow entropy neutron star equation of state modified gravity singularities gravitational collapse accretion rate event horizon stability Chandrasekhar limit logarithmic correction gravastar area law gravitational interaction accretion disk hawking radiation mechanism schwarzschild metric ringdown tidal charge