Non-axisymmetric instability and fragmentation of general relativistic quasi-toroidal stars

In a recent publication, we have demonstrated that differentially rotating stars admit new channels of black hole formation via fragmentation instabilities. Since a higher order instability of this kind could potentially transform a differentially rotating supermassive star into a multiple black hole system embedded in a massive accretion disk, we investigate the dependence of the instability on parameters of the equilibrium model. We find that many of the models constructed exhibit non-axisymmetric instabilities with corotation points, even for low values of T/|W|, which lead to a fission of the stars into one, two or three fragments, depending on the initial perturbation. At least in the models selected here, an m=1 mode becomes unstable at lower values of T/|W|, which would seem to favor a scenario where one black hole with a massive accretion disk forms. In this case, we have gained evidence that low values of compactness of the initial model can lead to a stabilization of the resulting fragment, thus preventing black hole formation in this scenario.