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要旨

We present the first calculation of gravitational wave emission produced in the gravitational collapse of uniformly rotating neutron stars to black holes in fully three-dimensional simulations. The initial stellar models are relativistic polytropes which are dynamically unstable and with angular velocities ranging from slow rotation to the mass-shedding limit. An essential aspect of these simulations is the use of progressive mesh-refinement techniques which allow to move the outer boundaries of the computational domain to regions where gravitational radiation attains its asymptotic form. The waveforms have been extracted using a gauge-invariant approach in which the numerical spacetime is matched with the non-spherical perturbations of a Schwarzschild spacetime. Overall, the results indicate that the waveforms have features related to the properties of the initial stellar models (in terms of their w-mode oscillations) and of the newly produced rotating black holes (in terms of their quasi-normal modes). While our waveforms are in good qualitative agreement with those computed by Stark and Piran in two-dimensional simulations, our amplitudes are about one order of magnitude smaller and this difference is mostly likely due to our less severe pressure reduction. For a neutron star rotating uniformly near mass-shedding and collapsing at 10 kpc, the signal-to-noise ratio computed uniquely from the burst is S/N ~ 0.25, but this grows to be S/N <~ 4 in the case of LIGO II.