The radiative stress tensor

We use the transfer equation in relativistic form to develop an expansion o f the one-photon distribution for a medium with constant photon mean free p ath, epsilon. On carrying out appropriate integrations and manipulations, w e convert this expansion into one for the frequency-integrated intensity. W e regroup the terms of the intensity expansion according to both the power of epsilon and the angular structure of the various terms and then carry ou t angle integrations to obtain the expansions for the components of the str ess energy tensor: the radiative energy density, the radiative flux, and th e pressure tensor. In leading order, we recover Thomas' results for the vis cosity tensor and his expression for the viscosity coefficient, which are c orrect for short mean free paths. As had been done earlier for the radiativ e heat equation, we keep at each order in the expansion a dominant portion, but this time one with a richer angular structure. Then, after some rearra ngement of the various summations in the expressions for the moments, we re place the sum of the calculated higher order terms by a Padi approximant, o r rational approximation, to provide an improved closure approximation for the radiative stress tensor. The resulting radiative viscosity tensor may b e expressed either as a simple integral operator acting on the Thomas stres s tensor or as the solution of an inhomogenous, linear partial differential equation. The expression obtained for the radiative viscosity tensor appli es for media with long, as well as short, photon mean free paths. We also d evelop results applicable for relatively smooth flows by using the form of the Thomas stress tensor with generalized transport coefficients derived by the application of a suitable operator to the bare Thomas coefficients.