Three-dimensional simulations of distorted black holes. I. Comparison with axisymmetric results

TL;DR

This paper demonstrates the successful 3D numerical evolution of distorted black holes, comparing results with axisymmetric models, and shows accurate gravitational wave extraction even for complex modes, advancing numerical relativity techniques.

Contribution

It provides a detailed comparison between 3D and axisymmetric simulations of distorted black holes, validating 3D methods for gravitational wave extraction and black hole dynamics.

Findings

3D simulations accurately reproduce axisymmetric results.

Gravitational waves can be extracted with high precision from 3D data.

Higher mode waveforms (l=4,6) are successfully computed and compared.

Abstract

We consider the numerical evolution of black hole initial data sets, consisting of single black holes distorted by strong gravitational waves, with a full 3D, nonlinear evolution code. These data sets mimic the late stages of coalescing black holes. We compare various aspects of the evolution of axisymmetric initial data sets, obtained with this 3D code, to results obtained from a well established axisymmetric code. In both codes we examine and compare the behavior of metric functions, apparent horizon properties, and waveforms, and show that these dynamic black holes can be accurately evolved in 3D. 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 when they carry away only a small fraction ($<< 1%$) of the rest mass energy of the system. Waveforms for both the $\ell=2$ and the much more difficult $\ell=4$ and $\ell=6$ 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.