Evolution of Rotating Supermassive Stars to the Onset of Collapse

We launch a fully relativistic study of the formation of supermassive blackholes via the collapse of supermassive stars. Here we initiate ourinvestigation by analyzing the secular evolution of supermassive stars up tothe onset of dynamical instability and collapse. We focus on the effects ofrotation, assumed uniform, and general relativity. We identify the criticalconfiguration at which radial instability sets in and determine its structurein detail. We show that the key nondimensional ratios R/M, T/|W| and J/M^2 (Tis the rotational kinetic energy and W is the gravitational potential energy)for this critical configuration are universal numbers, independent of the mass,spin, radius or history of the star. We compare results from an approximate,analytic treatment with a fully relativistic, numerical calculation and findgood agreement. We solve analytically for the time evolution of theseparameters up to the onset of instability. Cooling by photon radiation drivesthe evolution, which is accompanied by mass, angular momentum and entropy loss.The critical configuration serves as initial data for a future relativistic,hydrodynamical, 3D simulation of the collapse of an unstable supermassive star.Since this implosion starts from a universal critical configuration, thecollapse is also uniquely determined and should produce a universalgravitational waveform. In this paper we briefly speculate on the possibleoutcome of this collapse and asses to what extent it offers a promising routeto forming a supermassive black hole.Comment: 13 pages, 6 figures, uses emulateapj.sty; to appear in Ap