Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A detailed proof of the fundamental theorem of STF multipole expansion
  in linearized gravity   The linearized field equations of general relativity in harmonic coordinates
are given by an inhomogeneous wave equation. In the region exterior to the
matter field, the retarded solution of this wave equation can be expanded in
terms of 10 Cartesian symmetric and tracefree (STF) multipoles in
post-Minkowskian approximation. For such a multipole decomposition only three
and rather weak assumptions are required:
  1. No-incoming radiation condition.
  2. The matter source is spatially compact.
  3. A spherical expansion for the metric outside the matter source is
possible.
  During the last decades, the STF multipole expansion has been established as
a powerful tool in several fields of gravitational physics: celestial
mechanics, theory of gravitational waves and in the theory of light propagation
and astrometry. But despite its formidable importance, an explicit proof of the
fundamental theorem of STF multipole expansion has not been presented thus far,
while only some parts of it are distributed into several publications. In a
technical but more didactical form, an explicit and detailed mathematical proof
of each individual step of this important theorem of STF multipole expansion is
represented.

11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn