We compute gravitational waves emitted by the collapse of a rotating very massive star ( VMS ) core leading directly to a black hole in axisymmetric numerical-relativity simulations .
The evolved rotating VMS is derived by a stellar evolution calculation and its initial mass and the final carbon-oxygen core mass are 320 M _ { \odot } and \approx 150 M _ { \odot } , respectively .
We find that for the moderately rapidly rotating cases , the peak strain amplitude and the corresponding frequency of gravitational waves are \sim 10 ^ { -22 } and f \approx 300 –600 Hz for an event at the distance of D = 50 Mpc .
Such gravitational waves will be detectable only for D \alt 10 Mpc by second generation detectors , advanced LIGO , advanced VIRGO , and KAGRA , even if the designed sensitivity for these detectors is achieved .
However , third-generation detectors will be able to detect such gravitational waves for an event up to D \sim 100 Mpc .
The detection of the gravitational-wave signal will provide a potential opportunity for verifying the presence of VMSs with mass \agt 300 M _ { \odot } and their pair-unstable collapse in the universe .