Numerical Evolution of Dynamic 3D Black Holes: Extracting Waves

TL;DR

This paper demonstrates the accurate 3D numerical evolution of dynamic black holes distorted by gravitational waves, enabling precise extraction of emitted waveforms and providing benchmarks for future black hole simulations.

Contribution

It introduces a full 3D nonlinear evolution code capable of accurately simulating distorted black holes and extracting gravitational waves, including higher-order modes.

Findings

Successful 3D evolution of distorted black holes

Accurate extraction of gravitational waveforms, including $ ext{l}=2$ and $ ext{l}=4$ modes

Validation against axisymmetric codes confirming reliability

Abstract

We consider the numerical evolution of dynamic black hole initial data sets with a full 3D, nonlinear evolution code. These data sets consist of single black holes distorted by strong gravitational waves, and mimic the late stages of coalescing black holes. Through comparison with results from well established axisymmetric codes, we show that these dynamic black holes can be accurately evolved. In particular, we show that with present computational resources and techniques, the process of excitation and ringdown of the black hole can be evolved, and one can now extract accurately the gravitational waves emitted from the 3D Cartesian metric functions, even though they may be buried in the metric at levels on the order of $10^{-3}$ and below. Waveforms for both the $\ell=2$ and the much more difficult $\ell=4$ modes are computed and compared with axisymmetric calculations. In addition to exploring the physics of distorted black hole data sets, and showing the extent to which the waves can be accurately extracted, these results also provide important testbeds for all fully nonlinear numerical codes designed to evolve black hole spacetimes in 3D, whether they use singularity avoiding slicings, apparent horizon boundary conditions, or other evolution methods.