  We present a method for analyzing the interaction between radiation and
matter in regions of intense, relativistic shear that can arise in many
astrophysical situations. We show that there is a simple velocity profile that
should be manifested in regions of large shear that have "lost memory" of their
boundary conditions, and we use this self-similar velocity profile to construct
the surface of last scattering, or $\tau \simeq 1$ surface, as viewed from any
comoving point within the flow. We demonstrate that a simple treatment of
scattering from this $\tau \simeq 1$ surface exactly conserves photon number,
and derive the rate at which the radiation field is heated due to the shear
present in the flow. The components of the comoving radiation energy-momentum
tensor are calculated, and we show that they have relatively simple,
approximate forms that interpolate between the viscous (small shear) and
streaming (large shear) limits. We put our expression for the energy-momentum
tensor in a covariant form that does not depend on the explicit velocity
profile within the fluid and, therefore, represents a natural means for
analyzing general, radiation-dominated, relativistic shear flows.
