Hydrodynamic gradient expansion in linear response theory

A foundational question in relativistic fluid mechanics concerns the properties of hydrodynamic gradient expansion at large orders. We establish precise conditions under which this diverges for a broad class microscopic theories admitting limit, linear regime. Our result does not rely on highly symmetric flows utilized by previous studies heavy-ion collisions and cosmology. The whenever energy density or velocity fields have support momentum space exceeding critical momentum, converges otherwise. This is an intrinsic property theory set branch point singularities dispersion relations.