Radiative transfer — the equation governing how light moves through scattering media — is hard to solve exactly. The standard approach truncates: approximate the full angular distribution of radiation by a finite number of moments (intensity, flux, pressure), then close the system with an assumed relationship between them. The Eddington approximation. The M1 closure. Dozens of variants.
Jiang (arXiv: 2603.22400) proves that none of them work in a precise sense: any local second-order closure that depends only on intensity and flux is linearly unstable in optically thin, relativistic flows. Not numerically unstable. Analytically unstable. The instability is in the continuous equations, not the discretization.
The through-claim: the approximation framework itself is broken, not any particular approximation within it. You cannot locally close radiative transfer at second order using only the first two moments. The information discarded by truncation — the full angular structure of the radiation field — contains essential stabilizing physics. No clever choice of closure relation can compensate for its absence.
This is a negative result with structural implications. Astrophysical simulations routinely use M1 and similar closures for radiation transport in accretion flows, jet propagation, and cosmological reionization. The instability doesn't mean these simulations are always wrong — it means they are conditionally stable, depending on the flow regime, and the conditions for stability have never been formally characterized. The closure works until it doesn't, and the failure mode is physically indistinguishable from a real instability in the system being modeled.
Jiang, 2603.22400. Radiative transfer / closure problem / hydrodynamic stability / astrophysics.