How Pressure Stops Black Holes from Being Born express
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.
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.
Original abstract
as written by the authors arXiv:2606.29590
The threshold and scaling laws of gravitational critical collapse depend sensitively on the matter equation of state. We investigate how these quantities are modified by a generic feature of dense matter that is absent from the radiation fluid commonly assumed in primordial black hole (PBH) studies: pressure stiffening as a maximum density is approached. As an analytically tractable proxy, we adopt the closed-form equation of state of a single-occupancy lattice gas, \(p=-T\ln(1-\rho)\), which exhibits a density-dependent sound speed and a saturation density. Using general-relativistic simulations of spherically symmetric collapse, we show that this nonlinear pressure feedback increases the PBH formation threshold by \(0.50\pm0.02\%\) relative to the radiation equation of state within the causal regime of the model. At the same time, the critical mass-scaling exponent remains \(\gamma=0.357\pm0.001\), consistent with the radiation-fluid value to within our numerical precision. This agreement reflects the fact that the lattice equation of state approaches the radiation fluid at low density and remains only a mild perturbation over the near-critical regime, rather than indicating a universal critical exponent. Our results provide a proof of principle that saturation-induced stiffening can stabilize gravitational collapse and shift the PBH threshold, while introducing a linear-response framework for assessing the impact of more realistic equations of state on primordial black hole formation.
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