The Ultimate Stiffness Limit of Neutron Stars ⚡ экспресс
The equation of state parameter φ ≡ P/ε determines the response of matter to extreme compression. Its value at the center of the most massive neutron star, φ_c, sets a universal upper density limit for all visible matter, which, due to the nonlinearity of GR, turns out to be much lower than the naive limit of special relativity (φ=1). In this work, the theoretical upper bound on φ_c is refined by self-consistently accounting for the mass-shell stability condition near the stellar center alongside the causality constraint. An analysis within the IPAD-TOV framework yields an improved estimate φ_c ≲ 0.385, slightly exceeding the previously obtained limit of 0.374 but fully compatible with it. A refined scaling relation for neutron star compactness is also derived, the universality of which is verified for 284 realistic equations of state that include first-order phase transitions and exotic components. The obtained limit opens a model-independent window into the microphysics of cold, ultra-dense matter in a strong gravitational field.
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.