Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proposal of a gauge-invariant treatment of l=0,1-mode perturbations on
  Schwarzschild Background Spacetime   A gauge-invariant treatment of the monopole- ($l=0$) and dipole ($l=1$) modes
in linear perturbations of the Schwarzschild background spacetime is proposed.
Through this gauge-invariant treatment, we derived the solutions to the
linearized Einstein equation for these modes with a generic matter field. In
the vacuum case, these solutions include the Kerr parameter perturbations in
the $l=1$ odd modes and the additional mass parameter perturbations of the
Schwarzschild mass in the $l=0$ even modes. The linearized version of
Birkhoff's theorem is also confirmed in a gauge-invariant manner. In this
sense, our proposal is reasonable.

22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg