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Phys. Rev. D 53, 6881 - 6888 (1996)

Zel’dovich-type approximation for an inhomogeneous universe in general relativity: Second-order solutions

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Heinz Russ, Masaaki Morita, Masumi Kasai, and Gerhard Börner
Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
Department of Physics, Hirosaki University, 3 Bunkyo-cho, Hirosaki, 036 Japan
Max-Planck Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85740 Garching, Germany

Received 11 December 1995

The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those given in the Lagrangian perturbation theory in Newtonian cosmology. Neglecting the cosmological constant and assuming a flat background model we give the solutions of the nonlinear dynamics of cosmological perturbations. We present the complete second-order solutions, which extend and improve earlier works. © 1996 The American Physical Society.


©1996 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevD.53.6881
DOI: 10.1103/PhysRevD.53.6881
PACS: 98.80.Hw, 04.25.Nx

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