Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Petrov types of slowly rotating fluid balls   Circularly rotating axisymmetric perfect fluid space-times are investigated
to second order in the small angular velocity. The conditions of various
special Petrov types are solved in a comoving tetrad formalism. A number of
theorems are stated on the possible Petrov types of various fluid models. It is
shown that Petrov type II solutions must reduce to the de Sitter spacetime in
the static limit. Two space-times with a physically satisfactory
energy-momentum tensor are investigated in detail. For the rotating
incompressible fluid, it is proven that the Petrov type cannot be D. The
equation of the rotation function $\omega $ can be solved for the Tolman type
IV fluid in terms of quadratures. It is also shown that the rotating version of
the Tolman IV space-time cannot be Petrov type D.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph