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We explore a possible scenario of the explosion as a result of core collapsesof rotating massive stars that leave a black hole by performing aradiation-viscous-hydrodynamics simulation in numerical relativity. We takemoderately and rapidly rotating compact pre-collapse stellar models derived instellar evolution calculations as the initial conditions. We find that theviscous heating in the disk formed around the central black hole powers anoutflow. For rapidly rotating models, the explosion energy is $\gtrsim3\times10^{51}$ erg, which is comparable to or larger than that of typicalstripped-envelope supernovae, indicating that a fraction of such supernovae maybe explosions powered by black-hole accretion disks. The explosion energy isstill increasing at the end of the simulations with a rate of $>10^{50}$ erg/s,and thus, it may reach $\sim10^{52}$ erg. The nucleosynthesis calculation showsthat the mass of $^{56}$Ni amounts to $\gtrsim 0.1M_\odot$, which, togetherwith the high explosion energy, satisfies the required amount for broad-linedtype Ic supernovae. The moderately rotating models predict small ejecta mass oforder $0.1M_\odot$ and explosion energy of $\lesssim 10^{51}$ erg. Due to thesmall ejecta mass, these models may predict a short-timescale transient withthe rise time 3$-$5 d. It can lead to a bright ($\sim10^{44}$ erg/s) transientlike superluminous supernovae in the presence of dense massive circum-stellarmedium. Irrespective of the models, the lowest value of the electron fractionof the ejecta is $\gtrsim 0.4$, and thus, the synthesis of heavy $r$-processelements is not found in our calculation.

Collapse of rotating massive stars leading to black hole formation and energetic supernovae