Black Hole-Black Hole Binary Merger Simulations in Full General
Yuk Tung Liu
Stuart L. Shapiro
Thomas W. Baumgarte
University of Illinois at Urbana-Champaign
The calculation of a binary black hole inspiral and
coalescence is one of the great triumphs of numerical relativity. The
successful solution to this problem has required contributions from many
people working over many years. The chief ingredients include a stable
algorithm to solve Einstein's field equations in 3+1 dimensions, valid
initial data for two black holes in quasiequilibrium circular orbit, a
means of avoiding the black hole spacetime singularity on the
computational grid, a good gauge choice for performing the evolution,
and adaptivity to achieve high resolution both in the strong-field
region near the black holes and in the far zone where the gravitational
waves are measured. By now, solving binary black hole coalescence on
computers has become almost routine.
By simulating the gravitational radiation waveforms from black hole-black hole (BHBH) mergers, we hope to test strong-field general relativity by comparing theoretical waveform templates with measurements made by ground-based laser interferometers like LIGO (Laser Inteferometer Gravitational Wave Observatory), VIRGO, GEO, and TAMA, and space-based interferometers like LISA (Laser Interferometer Space Antenna). These numerical calculations are especially important because BHBH binaries are expected to be among the most promising sources of gravitational waves. Also, BHBH merger calculations serve as a warm-up for the calculations of binary black hole-neutron star (BHNS) mergers. BHNS merger calculations are more challenging because of the presence of hydrodynamic matter.
The representative BHBH calculation summarized here was performed with the Illinois relativistic hydrodynamics code with the hydrodynamics turned "off" to solve the pure vacuum problem. The code utilizes the BSSN scheme for evolving the Einstein equations and employs AMR (adaptive mesh refinement). The initial data is "puncture" data for a BHBH binary in a quasicircular orbit and the evolution is performed with "moving puncture" gauge conditions.
Scientific visualization by