From the viewpoint of the comoving observer
we have analytically examined the Eddington factor
in the relativistic flow accelerating in the vertical direction;
we have introduced the one-tau photo-oval observed by the comoving observer,
and then calculated the comoving radiation fields and the Eddington factor.
The comoving radiation fields observed by the comoving observer
becomes anisotropic, and the Eddington factor must deviate from
the value for the isotropic radiation fields.
We found that the Eddington factor depends on
the velocity gradient as well as the flow velocity.
In the sufficiently optically thick linear regime,
the Eddington factor is analytically expressed as
$f (\tau, \beta, \frac{d\beta}{d\tau})
= \frac{1}{3} ( 1 + \frac{16}{15} \frac{d\beta}{d\tau})$,
where $\tau$ is the optical depth and
$\beta$ ($=v/c$) is the flow speed normalized by the speed of light.
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