1993/09/01 by Thomas Buchert, Jϋrgen Ehlers · 143 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Solar and Space Plasma Dynamics #Pulsars and Gravitational Waves Research #Physics #Conservative vector field #Instability #Perturbation theory (quantum mechanics) #Gravitational collapse #Classical mechanics #Gravitation #Perturbation (astronomy) #Isotropy #Mechanics #Compressibility #Quantum mechanics
paper · open access · doi:10.1093/mnras/264.2.375
published in Monthly Notices of the Royal Astronomical Society 264(2), 375-387 (Oxford University Press)
openalex publication_date 1993/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
A large class of solutions for second-order irrotational perturbations is derived in the framework of the Lagrangian theory of gravitational instability of a homogeneous and isotropic universe investigated in earlier papers. The solutions are evaluated in detail for perturbations in a flat background universe. The form of the solutions is designed for use in studies of the formation of large-scale structure from generic initial conditions. Some general remarks on the properties of the solutions are made. The result is illustrated by a special case and discussed. In particular, it is found that sheetlike structures stay compact after shell-crossing (as in the competing ‘adhesion model’), and that the collapse of first objects occurs earlier (as expected from numerical simulations) in the second-order approach. Both these properties compensate shortcomings of the ‘Zel’dovich approximation’. In contrast to the ‘adhesion model’, the nth-order Lagrangian perturbation solutions also describe internal structures of self-gravitating pancakes ( = 2n + 1 stream systems) in terms of the nth orbit crossings within pancakes.