Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational Waves from a Particle in Circular Orbits around a
  Schwarzschild Black Hole to the 22nd Post-Newtonian Order   We extend our previous results of the 14th post-Newtonian (PN) order
expansion of gravitational waves for a test particle in circular orbits around
a Schwarzschild black hole to the 22PN order, i.e. $v^{44}$ beyond the leading
Newtonian approximation where $v$ is the orbital velocity of a test particle.
Comparing our 22PN formula for the energy flux with high precision numerical
results, we find that the relative error of the 22PN flux at the innermost
stable circular orbit is about $10^{-5}$. We also estimate the phase difference
between the 22PN waveforms and numerical waveforms after a two-year inspiral.
We find that the dephase is about $10^{-9}$ for $\mu/M=10^{-4}$ and $10^{-2}$
for $\mu/M=10^{-5}$ where $\mu$ is the mass of the compact object and $M$ the
mass of the central supermassive black hole. Finally, we construct a hybrid
formula of the energy flux by supplementing the 4PN formula of the energy flux
for circular and equatorial orbits around a Kerr black hole with all the
present 22PN terms for the case of a Schwarzschild black hole. Comparing the
hybrid formula with the the full numerical results, we examine the performance
of the hybrid formula for the case of Kerr black hole.

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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph