- Zachariah B. Etienne
- Yuk Tung Liu
- Stuart L. Shapiro
- Thomas W. Baumgarte

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 calculations summarized here were 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.

Black hole-neutron star (BHNS) binary mergers are candidate engines for
generating both short-hard gamma-ray bursts (SGRBs) and detectable gravitational
waves. Using our most recent conformal thin-sandwich BHNS initial data and our fully
general relativistic hydrodynamics code, which is now AMR-capable, we are able to
efficiently and accurately simulate these binaries from large separations through
inspiral, merger, and ringdown. We evolve the metric using the BSSN formulation with
the standard moving puncture gauge conditions and handle the hydrodynamics with a
high-resolution shock-capturing scheme. We explore the effects of BH spin (aligned
and anti-aligned with the orbital angular momentum) by evolving three sets of initial
data with BH:NS mass ratio q=3: the data sets are nearly identical, except the BH
spin is varied between S_{BH}/M_{BH}^{2} = -0.5 (anti-aligned), 0.0,
and 0.75. The number of orbits before merger increases with S_{BH}/M_{BH}^{2}, as expected. We also
study the nonspinning BH case in more detail, varying q between 1, 3, and 5. We
calculate gravitational waveforms for the cases we simulate and compare them to
binary black-hole waveforms. Only a small disk (<
0.01 M_{sun}) forms for the anti-aligned spin case (S_{BH}/M_{BH}^{2} = -0.5) and for the most extreme mass ratio case (q=5). By
contrast, a massive (M_{disk} is about 0.2 M_{sun}), hot disk forms
in the rapidly spinning (S_{BH}/M_{BH}^{2} = 0.75) aligned BH case.
Such a disk could drive a SGRB, possibly by, e.g., producing a copious flux of
neutrino-antineutino pairs. Here we show the case with q=3 and S_{BH}/M_{BH}^{2} = 0.

Phys.Rev.D79:044024 (2009), arXiv:0812.2245v2

- Anthony Chan
- Stephen Drake
- Miaotianzi Jin
- David Kolschowsky
- David Kotan

- BHBH without spin
- S
_{BH}/ M_{BH}^{2}= 0.00, mass ratio q = 1.00 - BHBH with spin
- S
_{BH}/ M_{BH}^{2}= 0.85, mass ratio q = 1.00 - BHNS
- S
_{BH}/ M_{BH}^{2}= 0.00, mass ratio q = 3.00