Physics
Scientific paper
Nov 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phrvd..52.5605k&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 52, Issue 10, 15 November 1995, pp.5605-5611
Physics
29
Post-Newtonian Approximation, Perturbation Theory, Related Approximations
Scientific paper
A new approximation scheme in general relativity is developed to describe nonlinear inhomogeneous universes containing irrotational dust. The parallel-transported basis of the orthonormal tetrad frame is employed and a second-order differential equation is obtained for the perturbations of the spatial basis vectors, with nonlinear corrections as a source term. The equation can be solved iteratively in a way very similar to that in the Lagrangian perturbation theory in Newtonian cosmology. The first-order solution is presented, which contains Szekeres' exact solution as a special case. A general relativistic version of the ``Zel'dovich approximation'' is proposed with emphasis on the formal similarity to the Newtonian treatment.
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