Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of the second-order gravitational perturbations produced by
  a compact object   Accurate calculation of the gradual inspiral motion in an extreme mass-ratio
binary system, in which a compact-object inspirals towards a supermassive
black-hole requires calculation of the interaction between the compact-object
and the gravitational perturbations that it induces. These metric perturbations
satisfy linear partial differential equations on a curved background spacetime
induced by the supermassive black-hole. At the point particle limit the
second-order perturbations equations have source terms that diverge as
$r^{-4}$, where $r$ is the distance from the particle. This singular behavior
renders the standard retarded solutions of these equations ill-defined. Here we
resolve this problem and construct well-defined and physically meaningful
solutions to these equations. We recently presented an outline of this
resolution [E. Rosenthal, Phys. Rev. D 72, 121503 (2005)]. Here we provide the
full details of this analysis. These second-order solutions are important for
practical calculations: the planned gravitational-wave detector LISA requires
preparation of waveform templates for the expected gravitational-waves.
Construction of templates with desired accuracy for extreme mass-ratio binaries
requires accurate calculation of the inspiral motion including the interaction
with the second-order gravitational perturbations.

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ