  We examine the behavior of the variable Eddington factor for a
relativistically moving radiative flow in the vertical direction. We adopt the
"one-tau photo-oval" approximation in the comoving frame. Namely, the comoving
observer sees radiation coming from a closed surface where the optical depth
measured from the observer is unity; such a surface is called a one-tau
photo-oval. In general, the radiative intensity emitted by the photo-oval is
non-uniform and anisotropic. Furthermore, the photo-oval surface has a relative
velocity with respect to the comoving observer, and therefore, the observed
intensity suffers from the Doppler effect and aberration. In addition, the
background intensity usually depends on the optical depth. All of these
introduce the anisotropy to the radiation field observed by the comoving
observer. As a result, the relativistic Eddington factor $f$ generally depends
on the optical depth $\tau$, the four velocity $u$, and the velocity gradient
$du/d\tau$. % In the case of a plane-parallel vertical flow, we found that the
relativistic variable Eddington factor $f$ generally decreases as the velocity
gradient increases, but it increases as the velocity increases for some case.
When the comoving radiation field is uniform, it is well approximated by $3f
\sim 1/[ 1+ ({16}/{15})(-{du}/{\gamma d\tau}) +(-{du}/{\gamma d\tau})^{1.6-2}
  ]$. When the radiation field in the inertial frame is uniform, on the other
hand, it is expressed as $f = (1+3\beta^2)/(3+\beta^2$). These relativistic
variable Eddington factors can be used in various relativistic
radiatively-driven flows, such as black-hole accretion flows, relativistic
astrophysical jets and outflows, and relativistic explosions like gamma-ray
bursts.
