Gravitational-Wave Emission from Rotating Gravitational Collapse in Three Dimensions

We present the first three-dimensional (3D) calculations of the gravitational-wave emission in the collapse of uniformly rotating stars to black holes. The initial models are polytropes which are dynamically unstable and near the mass-shedding limit. The waveforms have been extracted using a gauge-invariant approach and reflect the properties of both the initial stellar models and of newly produced black holes, being in good qualitative agreement with those computed in previous 2D simulations. The wave amplitudes, however, are about 1 order of magnitude smaller, giving, for a source at 10 kpc, a signal-to-noise ratio $S/N\sim 0.25$ for LIGO-VIRGO and $S/N\lesssim 4$ for LIGO II.

Figure 1

The left panel shows the $\ell =2$, even-parity perturbation as extracted by observers at different positions $r_{\mathrm{ex}}$ expressed in retarded time. The right panel refers to the $\ell =4$ mode, with the inset offering a comparison in the amplitudes of the two modes.

Figure 2

Power spectra of the waveforms reported in Fig. 1. The dashed vertical lines indicate the frequencies of the QNMs of a black hole, while the dotted ones indicate the $w_1$ and $w_{\mathrm{II}}$ modes of a typical star.

Figure 3

TT gravitational-wave amplitudes extracted by the detector at $r_{\mathrm{ex}}=37.1M$ and for two different inclination angles.