  Stellar kinematics in the external regions of globular clusters can be used
to probe the validity of Newton's law in the low acceleration regimes without
the complication of non-baryonic dark matter. Indeed, in contrast with what
happens when studying galaxies, in globular clusters a systematic deviation of
the velocity dispersion profile from the expected Keplerian falloff would
provide indication of a breakdown of Newtonian dynamics rather than the
existence of dark matter. We perform a detailed analysis of the velocity
dispersion in the globular cluster omega Centauri in order to investigate
whether it does decrease monotonically with distance as recently claimed by
Sollima et al. (2009), or whether it converges toward a constant value as
claimed by Scarpa Marconi and Gilmozzi (2003B). We combine measurements from
these two works to almost double the data available at large radii, in this way
obtaining an improved determination of the velocity dispersion profile in the
low acceleration regime. We found the inner region of omega Centauri is clearly
rotating, while the rotational velocity tend to vanish, and is consistent with
no rotation at all, in the external regions. The cluster velocity dispersion at
large radii from the center is found to be sensibly constant. The main
conclusion of this work is that strong similarities are emerging between
globular clusters and elliptical galaxies, for in both classes of objects the
velocity dispersion tends to remain constant at large radii. In the case of
galaxies, this is ascribed to the presence of a massive halo of dark matter,
something physically unlikely in the case of globular clusters. Such
similarity, if confirmed, is best explained by a breakdown of Newtonian
dynamics below a critical acceleration.
