Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kinematics and Dynamics of $f(R)$ Theories of Gravity   We generalise the equations governing relativistic fluid dynamics given by
Ehlers and Ellis for general relativity, and by Maartens and Taylor for
quadratic theories, to generalised $f(R)$ theories of gravity. In view of the
usefulness of this alternative framework to general relativity, its
generalisation can be of potential importance for deriving analogous results to
those obtained in general relativity. We generalise, as an example, the results
of Maartens and Taylor to show that within the framework of general $f(R)$
theories, a perfect fluid spacetime with vanishing vorticity, shear and
acceleration is Friedmann--Lema\^{\i}tre--Robertson--Walker only if the fluid
has in addition a barotropic equation of state. It then follows that the
Ehlers--Geren--Sachs theorem and its ``almost'' extension also hold for $f(R)$
theories of gravity.

29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
16
The categories of this paper are: stat
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn