Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relativistic Zel'dovich approximation in spherically symmetric model   We compare relativistic approximation methods, which describe gravitational
instability in the expanding universe, in a spherically symmetric model. Linear
perturbation theory, second-order perturbation theory, relativistic Zel'dovich
approximation, and relativistic post-Zel'dovich approximation are considered
and compared with the Lema\^{\i}tre-Tolman-Bondi solution in order to examine
the accuracy of these approximations. We consider some cases of inhomogeneous
matter distribution while the homogeneous top-hat model has been usually taken
in the previous Newtonian works. It is found that the Zel'dovich-type
approximations are generally more accurate than the conventional perturbation
theories in the weakly nonlinear regime. Applicable range of the
Zel'dovich-type approximations is also discussed.

4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn