Non-Linear Relativistic Evolution of Cosmological Perturbations in Irrotational Dust

We report here second order perturbative Lagrangian computations of the collapse in irrotational dust fluid models and show that, on scales smaller than the horizon size, where the Newtonian Theory should apply, the magnetic tensor cannot be neglected in the general case. Only for perturbations on super-horizon scales the condition Hab = 0 condition would apply ( where Hab is the magnetic part of the Weyl tensor), leading to the preferential collapse of fluid elements to spindles, independently from the environmental conditions.