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We develop a new nonlinear method to model structure formation in generalrelativity from a generalization of the relativistic Lagrangian perturbationschemes, controlled by Szekeres (and LTB) exact solutions. The overall approachcan be interpreted as the evolution of a deformation field on an inhomogeneousreference model, obeying locally Friedmann-like equations. In the special caseof locally one-dimensional deformations, the new model contains the entireSzekeres family of exact solutions. As thus formulated, this approachparaphrases the Newtonian and relativistic Zel'dovich approximations, having alarge potential for applications in contexts where relativistic degrees offreedom are relevant. Numerical simulations are implemented to illustrate thecapabilities and accuracy of the model.

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