  We study the gravitational collapse of a rotating supermassive star (SMS) by
means of a (3+1) hydrodynamical simulation in a post-Newtonian (PN) approxi-
mation of general relativity. This problem is particularly challenging because
of the vast dynamical range in space which must be covered in the course of
col- lapse. We evolve a uniformly rotating SMS from the onset of radial
instability at R_{p}/M=411, where R_{p} is the proper polar radius of the star
and M is the total mass-energy, to the point at which the PN approximation
breaks down. We introduce a scale factor and a "comoving" coordinate to handle
the large varia- tion in radius during the collapse and focus on the central
core. Since T/W, the ratio of the rotational kinetic energy to the
gravitational binding energy, is nearly proportional to 1/R_{p} throughout the
collapse, the imploding star may ultimately exceed the critical value of T/W
for dynamical instability to bar-mode formation. However, for stars rotating
uniformly at the onset of col- lapse, we do not find any unstable growth of
bars prior to the termination of our simulation. We do find that the collapse
is likely to form a supermassive black hole (BH) coherently, with almost all of
the matter falling into the hole, leaving very little ejected matter to form a
disk. In the absence of nonaxi- symmetric bar formation, the collapse of a
uniformly rotating SMS does not lead to appreciable quasi-periodic
gravitational wave (GW) emission by the time our integrations terminate.
However, the coherent nature of the implosion suggests that rotating SMS
collapse will be a promising source of GW bursts. We also expect that,
following BH formation, long wavelength quasi-periodic waves will result from
quasi-normal ringing. These waves may be detectable by LISA.
