Black Hole Spectroscopy: Determining Waveforms from 3D Excited Black Holes

Abstract

We present the first results for Cauchy nonlinear evolution of 3D, nonaxisymmetric distorted black holes. We focus on the extraction and verification of 3D waveforms determined by numerical relativity. We show that the black hole evolution can be accurately followed through the ringdown period, and comparing with a recently developed perturbative evolution technique, we show that many waveforms in the black hole spectrum of modes, such as l=2 and l=4, including weakly excited nonaxisymmetric modes with m not zero, can be accurately evolved and extracted from the full nonlinear numerical evolution. We also identify new physics contained in higher modes, due to nonlinear effects. The implications for simulations related to gravitational wave astronomy are discussed.

Figures (5)

• Figure 1: We show waveforms for the $\ell=m=2$ nonaxisymmetric mode extracted from the full nonlinear 3D simulation of the distorted BH. The top graph shows the waveform extracted at different locations, while the bottom shows the phase-shifted waveforms, allowing comparison between them.
• Figure 2: We show the waveform for the $\ell=2,m=0$ mode, extracted from the linear and nonlinear evolution codes. The dotted (solid) line shows the linear (nonlinear) evolution.
• Figure 3: Waveforms are shown for the $\ell=4$, $m=0$ extracted from the linear and nonlinear evolution codes. The dotted (solid) line shows the linear (nonlinear) evolution.
• Figure 4: Waveforms are shown for the $\ell=4,m=2$ mode, extracted from the linear and nonlinear evolution codes. The dotted (solid) line shows the linear (nonlinear) evolution.
• Figure 5: Waveforms are shown for the $\ell=6,m=2$ mode, extracted from the linear and nonlinear evolution codes. The dotted (solid) line shows the linear (nonlinear) evolution. The discrepancy is attributed to a nonlinear effect.