  The collapse of massive rotating stellar cores and the associated accretion
onto the newborn compact object is thought to power long gamma ray bursts
(GRBs). The physical scale and dynamics of the accretion disk are initially set
by the angular momentum distribution in the progenitor, and the physical
conditions make neutrino emission the main cooling agent in the flow. The
formation and evolution of structure in these disks is potentially very
relevant for the energy release and its time variability, which ultimately
imprint on the observed GRB properties. To begin to characterize these, taking
into account the three dimensional nature of the problem, we have carried out
an initial set of calculations of the collapse of rotating polytropic cores in
three dimensions, making use of a pseudo-relativistic potential and a
simplified cooling prescription. We focus on the effects of self gravity and
cooling on the overall morphology and evolution of the flow for a given
rotation rate in the context of the collapsar model. For the typical cooling
times expected in such a scenario we observe the appearance of strong
instabilities on the cooling time scale following disk formation, which
modulate the properties of the flow. Such instabilities, and the interaction
they produce between the disk and the central object lead to significant
variability in the obtained mass accretion and energy loss rates, which will
likely translate into variations in the power of the relativistic outflow that
ultimately results in a GRB.
