Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newtonian Gravitational Multipoles as Group-Invariant Solutions   A family of vector fields that are the infinitesimal generators of determined
one-parameter groups of transformations are constructed. It is shown that these
vector fields represent symmetries of the system of differential equations
interrelated by the axially symmetric Laplace equation and a certain
supplementary equation. Group-invariant solutions of this system of equations
are obtained by means of two alternative methods, and it is proved that these
solutions turn out to be the family of axisymmetric potentials related to
specific gravitational multipoles. The existence of these symmetries provides
us with a generalization of the fact that the Newtonian Monopole is defined by
the solution of the Laplace equation with spherical symmetry, and it allows us
to extract from all solutions of this equation those with the prescribed
Newtonian Multipole Moments.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph