Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variables separation in gravity   To solve the problem of exact integration of the field equations or equations
of motion of matter in curved spacetimes one can use a class of Riemannian
metrics for which the simplest equations of motion can be integrated by the
complete separation of variables method. Here, we consider the particular case
of the class of Stackel metrics. These metrics admit integration of the
Hamilton-Jacobi equation for test particle by the complete separation of
variables method. It appears that the other important equations of motion
(Klein-Gordon-Fock, Dirac, Weyl) in curved spacetimes can be integrated by
complete separation of variables method only for the metrics, belonging to the
class of Stackel spaces.

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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math