We present results of full general relativistic (GR), three-dimensional (3D) core-collapse simulation of a massive star with multi-energy neutrino transport. Using a 70Mȯ zero-metallicity star, we show that the black-hole (BH) formation occurs at ∼ 300 ms after bounce. At a few ∼ 10 ms before the BH formation, we find that the stalled bounce shock is revived by neutrino heating from the forming hot proto-neutron star (PNS), which is aided by vigorous convection behind the shock. Our numerical results present the first evidence to validate the BH formation by the so-called fallback scenario. Furthermore we present results from a rapidly rotating core-collapse model of a 27Mȯ star that is trending towards an explosion. We point out that the correlated neutrino and gravitational-wave signatures, if detected, could provide a smoking-gun evidence of rapid rotation of the newly-born PNS.
