Non-separable perturbations of slowly rotating Friedmann-Robertson-Walker Type Brane-World Cosmological Models

In addition to the separable solutions of the rotation equation, relating the perturbations of the metric tensor to the angular velocity of the matter on the brane, we show that the rotation equation admits solutions for a special class of non-separable angular velocity of the matter distribution on the brane. The general solution of the rotation equation is expressed in terms of an arbitrary, spatial coordinate dependent function. By appropriately choosing the mathematical form of this function, several models of slowly rotating brane world Universes are obtained. In all cases the angular velocity of the matter and the metric rotation function tend, in the large time limit, to zero