  We analytically derive a relativistic variable Eddington factor in the
relativistic radiative flow, and found that the Eddington factor depends on the
{\it velocity gradient} as well as the flow velocity. When the gaseous flow is
accelerated and there is a velocity gradient, there also exists a density
gradient. As a result, an unobstructed viewing range by a comoving observer,
where the optical depth measured from the comoving observer is unity, is not a
sphere, but becomes an oval shape elongated in the direction of the flow; we
call it a {\it one-tau photo-oval}. For the comoving observer, an inner wall of
the photo-oval generally emits at a non-uniform intensity, and has a relative
velocity. Thus, the comoving radiation fields observed by the comoving observer
becomes {\it anisotropic}, and the Eddington factor must deviate from the value
for the isotropic radiation fields. % In the case of a plane-parallel vertical
flow, we examine the photo-oval and obtain the Eddington factor. In the
sufficiently optically thick linear regime, the Eddington factor is
analytically expressed as $f (\tau, \beta, \frac{d\beta}{d\tau}) = {1/3} (1 +
{16/15} \frac{d\beta}{d\tau})$, where $\tau$ is the optical depth and $\beta$
($=v/c$) is the flow speed normalized by the speed of light. %i.e., the
Eddington factor depends on the velocity gradient. We also examine the linear
and semi-linear regimes, and found that the Eddington factor generally depends
both on the velocity and its gradient.
