## 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 data.

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 data choices.

For more information, refer to 1808.07490 and 1808.08228