Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation

TL;DR

This paper introduces a new nonlinear relativistic model for structure formation based on exact solutions, extending previous perturbation schemes and capable of capturing complex inhomogeneities with high accuracy.

Contribution

It generalizes relativistic Lagrangian perturbation methods by incorporating Szekeres solutions, providing a more precise framework for modeling inhomogeneous structure formation in general relativity.

Findings

Model reproduces Szekeres solutions exactly in special cases.

Numerical simulations demonstrate high accuracy and potential applications.

Framework extends Zel'dovich approximations to relativistic regimes.

Abstract

We develop a new nonlinear method to model structure formation in general relativity from a generalization of the relativistic Lagrangian perturbation schemes, controlled by Szekeres (and LTB) exact solutions. The overall approach can be interpreted as the evolution of a deformation field on an inhomogeneous reference model, obeying locally Friedmann-like equations. In the special case of locally one-dimensional deformations, the new model contains the entire Szekeres family of exact solutions. As thus formulated, this approach paraphrases the Newtonian and relativistic Zel'dovich approximations, having a large potential for applications in contexts where relativistic degrees of freedom are relevant. Numerical simulations are implemented to illustrate the capabilities and accuracy of the model.