Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge-invariant perturbation theory on the Schwarzschild background
  spacetime Part III: -- Realization of exact solutions   This is the Part III paper of our series of papers on a gauge-invariant
perturbation theory on the Schwarzschild background spacetime. After reviewing
our general framework of the gauge-invariant perturbation theory and the
proposal on the gauge-invariant treatments for $l=0,1$ mode perturbations on
the Schwarzschild background spacetime in [K.~Nakamura, arXiv:2110.13508
[gr-qc]], we examine the problem whether the $l=0,1$ even-mode solutions
derived in the Part II paper [K.~Nakamura, arXiv:2110.13512 [gr-qc]] are
physically reasonable, or not. We consider the linearized versions of the
Lema\^itre-Tolman-Bondi solution and the C-metric. As the result, we show that
our derived even-mode solutions to the linearized Einstein equations actually
realize above two linearized solutions. This fact supports that our derived
solutions are physically reasonable, which implies that our proposal on the
gauge-invariant treatments for $l=0,1$ mode perturbations are also physically
reasonable. We also briefly summarize our conclusions of our series of papers.

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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th