Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact Star in General $F(R)$ Gravity: Inevitable Degeneracy Problem
  and Non-Integer Power Correction   We investigate a compact star in the general $F(R)$ gravity. Developing a
novel formulation in the spherically symmetric and static space-time with the
matter, we confirm that an arbitrary relation between the mass $M$ and the
radius $R_s$ of the compact star can be realized by adjusting the functional
form of $F(R)$. Such a degeneracy with a choice of the equation of state (EOS)
suggests that only mass-radius relation is insufficient to constrain the $F(R)$
gravity. Furthermore, by solving the differential equation for $\left.
\frac{dF(R)}{dR}\right|_{R=R(r)}$ near and inside the surface of the compact
star with the polytropic EOS, the boundary condition demands a weak curvature
correction to the Einstein gravity could be non-integer power of the scalar
curvature, which gives a stringent constraint on the functional form of
$F\left(R\right)$. This consequence follows that the equation of motion in
$F(R)$ gravity includes the fourth-order derivative of metric, and thus, it is
applicable to general $F(R)$ models.

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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg