Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relativistic Variable Eddington Factor   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.

14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th