The collapse of differentially rotating supermassive stars: Conformally flat simulations

We investigate the gravitational collapse of rapidly rotating relativistic supermassive stars by means of 3 + 1 hydrodynamic simulations in conformally flat spacetime of general relativity. We study the evolution of differ-entially rotating supermassive stars of q ≡ J/M² ∼ 1 (J is the angular momentum, and M is the gravitational mass of the star) from the onset of radial instability at R/M ∼ 65 (R is the circumferential radius of the star) to the point at which the conformally flat approximation breaks down. We find that the collapse of a star of q ≳ 1, a radially unstable differentially rotating star, forms a black hole of q ≲ 1. The main reason preventing formation of a black hole of q ≳ 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 or bar. In the absence of nonaxisymmetric deformation, the collapse of differentially rotating supermassive stars from the onset of radial instability are promising sources of burst and quasi-normal ringing waves seen with the Laser Interferometer Space Antenna.