Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order

Abstract

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given together with extensions and applications for accessing the nonperturbative regime. We furnish here construction rules to obtain from Newtonian solutions the gravitoelectric class of relativistic solutions, for which we give the complete perturbation and solution schemes at any order of the perturbations. By construction, these schemes generalize the complete hierarchy of solutions of the Newtonian Lagrangian perturbation theory.

17 pages, a few minor extensions to match the published version in PRD

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• The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by Jürgen Ehlers)
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• 3+1 formalism of the minimally extended varying speed of light model
• On the maximum volume of collapsing structures
• Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood
• Nonperturbative collapse models for collisionless self-gravitating flows
• Cosmological perturbations on an averaged background