H. Russ et al., ZELDOVICH-TYPE APPROXIMATION FOR AN INHOMOGENEOUS UNIVERSE IN GENERAL-RELATIVITY - 2ND-ORDER SOLUTIONS, Physical review. D. Particles and fields, 53(12), 1996, pp. 6881-6888
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.