*Black Hole-Black Hole Binary Merger in Full General Relativity*

** Zachariah B. Etienne
Yuk Tung Liu
Stuart L. Shapiro**

**ABSTRACT**

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 calculation summarized here was performed with the
Ilinois 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*

last updated 8 July 08 by AH