Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-force of a scalar field for circular orbits about a Schwarzschild
  black hole   The foundations are laid for the numerical computation of the actual
worldline for a particle orbiting a black hole and emitting gravitational
waves. The essential practicalities of this computation are here illustrated
for a scalar particle of infinitesimal size and small but finite scalar charge.
This particle deviates from a geodesic because it interacts with its own
retarded field $\psi^\ret$. A recently introduced Green's function $G^\SS$
precisely determines the singular part, $\psi^\SS$, of the retarded field. This
part exerts no force on the particle. The remainder of the field $\psi^\R =
\psi^\ret - \psi^\SS$ is a vacuum solution of the field equation and is
entirely responsible for the self-force. A particular, locally inertial
coordinate system is used to determine an expansion of $\psi^\SS$ in the
vicinity of the particle. For a particle in a circular orbit in the
Schwarzschild geometry, the mode-sum decomposition of the difference between
$\psi^\ret$ and the dominant terms in the expansion of $\psi^\SS$ provide a
mode-sum decomposition of an approximation for $\psi^\R$ from which the
self-force is obtained. When more terms are included in the expansion, the
approximation for $\psi^\R$ is increasingly differentiable, and the mode-sum
for the self-force converges more rapidly.

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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph