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

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Wiegand,  Alexander
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1503.02566.pdf
(Preprint), 346KB

PhysRevD.92_023512.pdf
(Any fulltext), 305KB

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Citation

Alles, A., Buchert, T., Roumi, F. A., & Wiegand, A. (2015). Lagrangian theory of structure formation in relativistic cosmology III: gravitoelectric perturbation and solution schemes at any order. Physical Review D, 92: 023512. doi:10.1103/PhysRevD.92.023512.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0026-BBF7-9
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 here furnish 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.