Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-order post-Newtonian expansion of the redshift invariant for
  eccentric-orbit non-spinning extreme-mass-ratio inspirals   We calculate the eccentricity dependence of the high-order post-Newtonian
(PN) series for the generalized redshift invariant $\langle u^t \rangle_\tau$
for eccentric-orbit extreme-mass-ratio inspirals on a Schwarzschild background.
These results are calculated within first-order black hole perturbation theory
(BHPT) using Regge-Wheeler-Zerilli (RWZ) gauge. Our \textsc{Mathematica} code
is based on a familiar procedure, using PN expansion of the
Mano-Suzuki-Takasugi (MST) analytic function formalism for $l$ modes up to a
certain maximum and then using a direct general-$l$ PN expansion of the RWZ
equation for arbitrarily high $l$. We calculate dual expansions in PN order and
in powers of eccentricity, reaching 10PN relative order and $e^{20}$. Detailed
knowledge of the eccentricity expansion at each PN order allows us to find
within the eccentricity dependence numerous closed-form expressions and
multiple infinite series with known coefficients. We find leading logarithm
sequences in the PN expansion of the redshift invariant that reflect a similar
behavior in the PN expansion of the energy flux to infinity. A set of flux
terms and special functions that appear in the energy flux, like the
Peters-Mathews flux itself, are shown to reappear in the redshift PN expansion.

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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex