Hyperbolic Initial Data for Boosted and Spinning Black Holes

The two-body problem in general relativity -- such as black hole mergers -- plays an important role in decoding the gravitational wave signals. This problem is unsolved analytically and is numerically challenging, because although when given correct initial data, the Einstein equations will yield the expected solution, they are very sensitive to numerical errors and could lead to wrong spacetimes. Standard techniques for constructing initial data use elliptic equations that require inner boundary conditions and are prone to `junk' radiation. We present work in progress to numerically implement and test a hyperbolic-algebraic method to solve the initial data constraints. This method, proposed by I. Racz, does not rely on conformal flatness and is mathematically well posed. We develop HyperSolID, a code that calculates Hyperbolic Solutions to Initial Data for black hole spacetimes. The numerical algorithm implements the Hamiltonian and momentum constraints as a system of well-posed, hyperbolic-algebraic equations in stereographic coordinates on a logarithmic grid. We test the code with two trials: a near-light-speed boosted Schwarzchild and high-spin Kerr black hole, in order to asses its performance with nontrivial spacetimes.