Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On analytic solutions of wave equations in regular coordinate systems on
  Schwarzschild background   The propagation of (massless) scalar, electromagnetic and gravitational waves
on fixed Schwarzschild background spacetime is described by the general
time-dependent Regge-Wheeler equation. We transform this wave equation to usual
Schwarzschild, Eddington-Finkelstein, Painleve-Gullstrand and Kruskal-Szekeres
coordinates. In the first three cases, but not in the last one, it is possible
to separate a harmonic time-dependence. Then the resulting radial equations
belong to the class of confluent Heun equations, i.e., we can identify one
irregular and two regular singularities. Using the generalized Riemann scheme
we collect properties of all the singular points and construct analytic (local)
solutions in terms of the standard confluent Heun function HeunC, Frobenius and
asymptotic Thome series. We study the Eddington-Finkelstein case in detail and
obtain a solution that is regular at the black hole horizon. This solution
satisfies causal boundary conditions, i.e., it describes purely ingoing
radiation at $r=2M$. To construct solutions on the entire open interval $r \,
\in \; ]0,\infty[ \,$, we give an analytic continuation of local solutions
around the horizon. Black hole scattering and quasi-normal modes are briefly
considered as possible applications and we use semi-analytically calculated
graybody factors together with the Damour-Ruffini method to reconstruct the
power spectrum of Hawking radiation emitted by the black hole.

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci