Shear in an expanding universe

Tetrad formalism has been used to investigate the growth of shear in a perturbed Friedmann universe with vanishing curvature. Perturbation theory for perfect fluids, exhibiting local rotational symmetry, has been developed and the resulting differential equations in second order shear perturbations have been integrated. The solutions are found to consist of two modes: one corresponding to linear perturbations which are monotonically decreasing with time, the other corresponding to non-linear perturbations which tend to increase in the Zeldovich universe, remain stationary during the radiation-dominated universe and decay slowly in the dust-filled universe.