The Ultimate Stiffness Limit of Neutron Stars express

Original: "A Universal Upper Bound on the Pressure-to-Energy Density Ratio in Neutron Stars"
· Bao-Jun Cai, Bao-An Li, Yu-Gang Ma
arXiv:2601.02980v1 · 2026-01-06 · CC0 1.0 · 1 min
The ratio of pressure to energy density in neutron stars cannot exceed 0.385 — that's the universal limit.

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Just as in a crowded room each new person sharply increases the pressure on the walls, in a neutron star increasing density leads to a rise in internal resistance. But even this resistance has an absolute ceiling. Physicists describe it with the ratio of pressure to energy density (the quantity φ) — a sort of measure of matter's "stubbornness." From special relativity, φ cannot exceed 1 anyway (otherwise signals inside the star would outpace the speed of light). And general relativity, adding spacetime curvature, tightens the limit even further. The key ingredient is the stability condition: the star's mass must increase from center to edge without gaps. With it, φ does not exceed 0.385. This number works for any conceivable star filling, from ordinary neutrons to quark soup. Surprisingly, the same law applies to water in a glass — it's just realized at negligible fractions of a percent, so we don't feel it.

A teaspoon of neutron star material weighs as much as Mount Everest.

\phi = P / \varepsilon
φ — the ratio of pressure (P) to energy density (ε), a kind of measure of matter's "stiffness."
Scientists
Subrahmanyan ChandrasekharJames JeansJocelyn Bell BurnellWolfgang PauliJohn Archibald WheelerRussell Hulse
Concepts
neutron star equation of state neutron star mass limit equation of state mass limit energy density superdense matter compactness null energy condition tev density of states gas constant effective number of neutrino species gravitational constant Bekenstein bound deuteron accretion rate super earth quark core envelope high pressure