The Cosmic Speed Limit for Neutron Stars ✛ ✦

Original: "Causality alone bounds the maximum radius difference between different-mass neutron stars"
· Aleksi Kurkela, Tuhin Malik
arXiv:2606.25186 · 2026-06-23 · CC BY 4.0 · 1 min
The speed of sound cannot exceed the speed of light: this simple law sets hard limits on the size of neutron stars.

A neutron star is the endpoint of stellar evolution after a supernova explosion. The remnant compresses so much that a teaspoon of its material weighs billions of tons. Fritz Zwicky predicted this in the 1930s, and Jocelyn Bell Burnell later discovered them as pulsars. The sound inside, a pressure wave, races at nearly the speed of light. But it can't outrun light. To keep the star from collapsing under gravity, the sound wave must make it from the center to the edge. It's like a relay race with a strict speed limit on the runners: the lap can't be too big, or the relay won't finish. Hence a simple rule: for a heavier star, the radius can't exceed the radius of a lighter one by more than 1.16 times minus a kilometer. Data from the NICER telescope confirmed: for the most massive pulsar, the radius shrank from 12.5 to 11.4 km. In the future, this limit will weed out errors and point to dark matter in the cores. Gravitational waves from mergers, caught by LIGO, will also be tested with this rule. Because of the monstrous density, spacetime around is curved, and the star acts as a gravitational lens.

Sound in a neutron star travels almost as fast as light — a million times faster than in water. A tiny pinch of this material on Earth's surface would cause a catastrophe, but its sound would circle the planet in an instant.

The sci-fi novel 'Dragon's Egg' [Robert Forward, Dragon's Egg] describes intelligent life on the surface of a neutron star. Causal constraints on the size of such objects hint at how compact their real arena must be.

R_{2.0}^{\max} = 1.16\, R_{1.4} - 1.1\ \text{km}
Linear radius relation following from causality
R_{2.0}^{\max} = 4.47\, \Lambda_{1.4}^{0.171}
Power-law dependence suitable for gravitational-wave data analysis
Scientists
Enrico FermiPaul DiracSubrahmanyan ChandrasekharHendrik LorentzIsidor Isaac RabiAlbert Einstein
Concepts
neutron star mass limit neutron star equation of state causality asteroid belt solar radius earth radius compactness equation of state radiation dose crust causal set theory neutron star structure stellar radius stellar radiation