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Abstract

We evolve high-mass disks of mass $15-50M_\odot$ orbiting a $50M_\odot$
spinning black hole in the framework of numerical relativity. Such high-mass
systems could be an outcome during the collapse of rapidly-rotating
very-massive stars. The massive disks are dynamically unstable to the so-called
one-armed spiral-shape deformation with the maximum fractional
density-perturbation of $\delta \rho/\rho \gtrsim 0.1$, and hence,
high-amplitude gravitational waves are emitted. The waveforms are characterized
by an initial high-amplitude burst with the frequency of $\sim 40-50$ Hz and
the maximum amplitude of $(1-10)\times 10^{-22}$ at the hypothetical distance
of 100 Mpc and by a subsequent low-amplitude quasi-periodic oscillation. We
illustrate that the waveforms in our models with a wide range of the disk mass
resemble that of GW190521. We also point out that gravitational waves from
rapidly-rotating very-massive stars can be the source for 3rd-generation
gravitational-wave detectors for exploring the formation process of
rapidly-rotating high-mass black holes of mass $\sim 50-100M_\odot$ in an early
universe.