Gravitational waves from supermassive stars collapsing to a supermassive black hole

We derive the gravitational waveform from the collapse of a rapidly rotating supermassive star (SMS) core leading directly to a seed of a supermassive black hole (SMBH) in axisymmetric numerical-relativity simulations. We find that the peak strain amplitude of gravitational waves emitted during the black hole formation is [approximate]5 x 10 super(-21) at the frequency [functionof] [approximate] 5mHz for an event at the cosmological redshift z= 3, if the collapsing SMS core is in the hydrogen-burning phase. Such gravitational waves will be detectable by space laser interferometric detectors like eLISA with signal-to-noise ratio [approximate] 10, if the sensitivity is as high as LISA for [functionof] = 1-10mHz. The detection of the gravitational wave signal will provide a potential opportunity for testing the direct-collapse scenario for the formation of a seed of SMBHs.