Effects of dark matter on the stability of supermassive stars

The stability of nonrotating supermassive stars (M > 10(5) M(.)) in the presence of a small dark matter component is examined. We find that the destabilizing effects of first-order nonlinear corrections from general relativity can be neutralized when a significant amount of nonrelativistic dark matter is present. In this case, it is possible for supermassive stars to be stabilized through the hydrogen-burning stage. Significant mass loss in this epoch might result in the ejection of the nucleosynthesis products of hot hydrogen burning. Ultimately, however, the post-Newtonian instability can only be delayed. If this instability occurs after the hydrogen-burning epoch, collapse of the star to a black hole is guaranteed.