The co-moving frame radiative transfer equation for spherically symmetric flows can be written as :
We set c=1; is the velocity; and is the usual Lorentz factor. Equation is a integro-differential equation, since the emissivity contains J_ , the zeroth angular moment of I_ :
and where is the source function, is the absorption opacity, and is the scattering opacity. With the assumption of time-independence and a monotonic velocity field Eq. 1 becomes a boundary-value problem in the spatial coordinate and an initial value problem in the frequency or wavelength coordinate. The equation can be written in operator form as: