Evolution of Rotating Supermassive Stars to the Onset of Collapse

Abstract

We launch a fully relativistic study of the formation of supermassive black holes via the collapse of supermassive stars. Here we initiate our investigation by analyzing the secular evolution of supermassive stars up to the onset of dynamical instability and collapse. We focus on the effects of rotation, assumed uniform, and general relativity. We identify the critical configuration at which radial instability sets in and determine its structure in detail. We show that the key nondimensional ratios R/M, T/|W|, and J/M² (T is 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 find good agreement. We solve analytically for the time evolution of these parameters up to the onset of instability. Cooling by photon radiation drives the evolution, which is accompanied by mass, angular momentum, and entropy loss. The critical configuration serves as initial data for a future relativistic, hydrodynamical, three-dimensional simulation of the collapse of an unstable supermassive star. Since this implosion starts from a universal critical configuration, the collapse is also uniquely determined and should produce a universal gravitational waveform. In this paper we briefly speculate on the possible outcome of this collapse and assess to what extent it offers a promising route to forming a supermassive black hole.