Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isotropy, shear, symmetry and exact solutions for relativistic fluid
  spheres   The symmetry method is used to derive solutions of Einstein's equations for
fluid spheres using an isotropic metric and a velocity four vector that is
non-comoving. Initially the Lie, classical approach is used to review and
provide a connecting framework for many comoving and so shear free solutions.
This provides the basis for the derivation of the classical point symmetries
for the more general and mathematicaly less tractable description of Einstein's
equations in the non-comoving frame. Although the range of symmetries is
restrictive, existing and new symmetry solutions with non-zero shear are
derived. The range is then extended using the non-classical direct symmetry
approach of Clarkson and Kruskal and so additional new solutions with non-zero
shear are also presented. The kinematics and pressure, energy density, mass
function of these solutions are determined.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics