Tetrad-based perturbative approach to inhomogeneous universes: a general relativistic version of the Zel'dovich approximation

A new approximate scheme in general relativity is developed to describe nonlinearly inhomogeneous universes containing irrotational dust. Parallelly transported basis of the orthonormal tetrad frame is employed and the 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 the way very similar to that in the Langrangian 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. It is also briefly discussed how to go beyond the Zel'dovich approximation in the general relativistic treatment. (orig.)Available from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman