Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational perturbations and metric reconstruction: Method of
  extended homogeneous solutions applied to eccentric orbits on a Schwarzschild
  black hole   We calculate the gravitational perturbations produced by a small mass in
eccentric orbit about a much more massive Schwarzschild black hole and use the
numerically computed perturbations to solve for the metric. The calculations
are initially made in the frequency domain and provide Fourier-harmonic modes
for the gauge-invariant master functions that satisfy inhomogeneous versions of
the Regge-Wheeler and Zerilli equations. These gravitational master equations
have specific singular sources containing both delta function and
derivative-of-delta function terms. We demonstrate in this paper successful
application of the method of extended homogeneous solutions, developed recently
by Barack, Ori, and Sago, to handle source terms of this type. The method
allows transformation back to the time domain, with exponential convergence of
the partial mode sums that represent the field. This rapid convergence holds
even in the region of $r$ traversed by the point mass and includes the
time-dependent location of the point mass itself. We present numerical results
of mode calculations for certain orbital parameters, including highly accurate
energy and angular momentum fluxes at infinity and at the black hole event
horizon. We then address the issue of reconstructing the metric perturbation
amplitudes from the master functions, the latter being weak solutions of a
particular form to the wave equations. The spherical harmonic amplitudes that
represent the metric in Regge-Wheeler gauge can themselves be viewed as weak
solutions. They are in general a combination of (1) two differentiable
solutions that adjoin at the instantaneous location of the point mass (a result
that has order of continuity $C^{-1}$ typically) and (2) (in some cases) a
delta function distribution term with a computable time-dependent amplitude.

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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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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: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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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: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg