  There are many hot discussions in the literature about two competing
paradigms in galactic and extra-galactic astronomy and cosmology, namely the
Dark Matter and the Modified Newtonian Dynamics (MOND). It is very difficult to
challenge MOND from the cosmological side because a full relativistic
realisation is needed in the first place, and any failure can then be
attributed to a particular model, and not to the MOND itself. We propose to
study non-relativistic stages of gravitational collapse in MOND which, we
argue, is a relevant task for this competition. Spherically symmetric dust
cloud collapse and intrinsic unavoidable non-linearities of the deep MOND
regime are discussed. We conclude that complicated, both numerical and
analytic, studies of modified gravitational dynamics are needed in order to
assess the viability of MOND.
