Three-dimensional simulations of distorted black holes: Comparison with axisymmetric results - art. no. 064019

We consider the numerical evolution of black hole initial data sets, consis ting 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 axi symmetric initial data sets, obtained with this 3D code, to results obtaine d from a well established axisymmetric code. In both codes we examine and c ompare the behavior of metric functions, apparent horizon properties, and w ave forms, and show that these dynamic black holes can be accurately evolve d in 3D. In particular we show that with present computational resources an d techniques the process of excitation and ringdown of the black hole can b e evolved, and one can now extract accurately the gravitational waves emitt ed from the 3D Cartesian metric functions, even when they carry away only a small fraction (much less than 1%) of the rest mass energy of the system. Wave forms for both the l=2 and the much more difficult l=4 and l=6 modes a re computed and compared with axisymmetric calculations. In addition to exp loring the physics of distorted black hole data sets, and showing the exten t to which the waves can be accurately extracted, these results also provid e important testbeds for all fully nonlinear numerical codes designed to ev olve black hole spacetimes in 3D, whether they use singularity avoiding sli cings, apparent horizon boundary conditions, or other evolution methods. [S 0556-2821(99)00506-8].