ZELDOVICH-TYPE APPROXIMATION FOR AN INHOMOGENEOUS UNIVERSE IN GENERAL-RELATIVITY - 2ND-ORDER SOLUTIONS

The gravitational instability of inhomogeneities in the expanding univ erse is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get e quations very similar to those given in the Lagrangian perturbation th eory in Newtonian cosmology. Neglecting the cosmological constant and assuming a flat background model we give the solutions of the nonlinea r dynamics of cosmological perturbations. We present the complete seco nd-order solutions, which extend and improve earlier works.