  We investigate some important physical aspects of a recently presented
interior solution for the Kerr metric. It is shown that, as in the spherically
symmetric case, there is a specific limit for the maximal value of the surface
potential (degree of compactness), beyond which, unacceptable physical
anomalies appear. Such a bound is related to the appearance of negative
(repulsive) gravitational acceleration, that is accompanied by the appearance
of negative values of the pressure. A detailed discussion on this effect is
presented. We also study the possibility of a fragmentation scenario, assuming
that the source leaves the equilibrium, and we bring out the differences with
the spherically symmetric case.
