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Abstract

We explore a possible scenario of the explosion as a result of core collapses
of rotating massive stars that leave a black hole by performing a
radiation-viscous-hydrodynamics simulation in numerical relativity. We take
moderately and rapidly rotating compact pre-collapse stellar models derived in
stellar evolution calculations as the initial conditions. We find that the
viscous heating in the disk formed around the central black hole powers an
outflow. For rapidly rotating models, the explosion energy is $\gtrsim
3\times10^{51}$ erg, which is comparable to or larger than that of typical
stripped-envelope supernovae, indicating that a fraction of such supernovae may
be explosions powered by black-hole accretion disks. The explosion energy is
still 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 shows
that the mass of $^{56}$Ni amounts to $\gtrsim 0.1M_\odot$, which, together
with the high explosion energy, satisfies the required amount for broad-lined
type Ic supernovae. The moderately rotating models predict small ejecta mass of
order $0.1M_\odot$ and explosion energy of $\lesssim 10^{51}$ erg. Due to the
small ejecta mass, these models may predict a short-timescale transient with
the rise time 3$-$5 d. It can lead to a bright ($\sim10^{44}$ erg/s) transient
like superluminous supernovae in the presence of dense massive circum-stellar
medium. Irrespective of the models, the lowest value of the electron fraction
of the ejecta is $\gtrsim 0.4$, and thus, the synthesis of heavy $r$-process
elements is not found in our calculation.