We investigate the gravitational collapse of rapidly rotating relativistic supermassive stars by means of a 3+1 hydrodynamical simulations in conformally flat spacetime of general relativity .
We study the evolution of differentially rotating supermassive stars of q \equiv J / M ^ { 2 } \sim 1 ( J is the angular momentum and M is the gravitational mass of the star ) from the onset of radial instability at R / M \sim 65 ( R is the circumferential radius of the star ) to the point where the conformally flat approximation breaks down .
We find that the collapse of the star of q \gtrsim 1 , a radially unstable differentially rotating star form a black hole of q \lesssim 1 .
The main reason to prevent formation of a black hole of q \gtrsim 1 is that quite a large amount of angular momentum stays at the surface .
We also find that most of the mass density collapses coherently to form a supermassive black hole with no appreciable disk nor bar .
In the absence of nonaxisymmetric deformation , the collapse of differentially rotating supermassive stars from the onset of radial instability are the promising sources of burst and quasinormal ringing waves in the Laser Interferometer Space Antenna .