Evolution and nucleosynthesis of very massive primordial stars

We investigate the evolution, final fate, and nucleosynthetic yields of rot ating and non-rotating very massive stars (VMS) of zero metallicity. First we address the issue of mass loss during hydrogen burning due to vibrationa l instabilities. We find that these objects are much more stable than what was found in previous studies of VMS of solar composition, and expect only negligible mass loss driven by the pulsations. As these stars thus reach th e end of their evolution with massive helium cores, they encounter the pair -creation instability. We find that for helium core masses of similar to 64 ...133 M-circle dot these stars are completely disrupted with explosion ene rgies of up to similar to 10(53) erg and eject up to similar to 60 M-circle dot of Ni-56. Stars with more massive helium cores collapse into black hol es. We present the first calculations that follow the collapse of such a ma ssive rotating star and predict that X-ray burst and significant gravitatio nal wave emission could result.