Binary black hole initial data
In order to solve Einstein's equations numerically, they are
first decomposed into a set of Constraint and Evolution equations.
The constraint equations do not have time derivatives and need to
be satisfied at any time in the simulation. The evolution
equations have first derivatives in time and are used to step
forward in time. However the evolutions equations preserve the
constraints (with caveats for NR), so we only need to solve the
constraints at the initial time. This is referred to as initial
In SpEC, evolutions are done in a gauge called the damped harmonic
gauge. This gauge has several nice properties and works very well
for mergers of binary black holes. However we do not currently
have a prescription to construct initial data in this gauge.
Instead we construct initial data by superposing two black holes in
Kerr-Schild coordinates and then solving the constraints. Then we do
a gauge transformation during the initial stages of evolution to
move smoothly into the damped harmonic gauge. However, this
introduces several unwanted dynamics and complications.
In this work, I construct initial data directly in the damped
harmonic gauge, so that we can avoid this gauge transformation.
This can help with various aspects such as reduction of spurious
junk radiation at the start of evolution, eccentricity reduction,
etc. This involves solving for a single black hole metric in the
damped harmonic gauge and superposing two such black holes before
solving the constraints. The idea is that, near each of the black
holes, the gauge is close to a single black hole damped harmonic
gauge. As a byproduct, I also construct initial data in the
harmonic gauge, which turns out to out perform all other initial
For more information, refer to