Solving the Initial Value Problem of two Black Holes

TL;DR

This paper introduces a new method for generating initial data for two black holes with arbitrary momentum, using Kerr-Schild slicing and a novel elliptic solver approach that simplifies numerical implementation.

Contribution

It presents a novel technique for solving elliptic equations in black hole initial data that avoids excision and employs Kerr-Schild slicing for more realistic configurations.

Findings

Successfully solves elliptic equations for two black holes with arbitrary momentum.

Provides more physically realistic initial data than previous conformally flat methods.

Simplifies numerical implementation by avoiding excision of singularities.

Abstract

We solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild spacetime slicing which provides more physically realistic solutions than the initial data based on conformally flat metric/maximal slicing methods. The singularity/inner boundary problems are circumvented by a new technique that allows the use of an elliptic solver on a Cartesian grid where no points are excised, simplifying enormously the numerical problem.