Causality constraints on radiative transfer

Abstract: The standard formula, due to Spiegel, for the smoothing of temperature fluctuations by radiative transfer is unstable in relativity. This is due to the fact that Spiegel neglected the transit time of light, thereby allowing the transport coefficients to move outside the convex geometry compatible with causality (the "hydrohedron"). Here, we fix this pathology. First, we prove that the linearized radiative transfer equations are causal and covariantly stable by construction. Then, we repeat Spiegel's calculation accounting for the finite speed of photons. We find that the full transfer problem can be solved analytically. All the infinite (exact) transport coefficients arising from it fall inside the hydrohedron. Our analysis also accounts for isotropic scattering.