Relativistic Zel'dovich approximation in spherically symmetric model

Details Relativistic Zel'dovich approximation in spherically symmetric model Relativistic Zel'dovich approximation in spherically symmetric model

1997-11-04

arxiv.org/abs/astro-ph/9711026v1

Phys.Rev. D57 (1998) 6094-6103; Erratum-ibid. D58 (1998) 089903

Astronomy and Astrophysics

Astrophysics

22 pages including 10 eps figures, REVTeX

Scientific paper

10.1103/PhysRevD.57.6094

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.

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