Quasi-equilibrium Binary Black Hole Initial Data for Dynamical Evolutions

TL;DR

This paper introduces a new formalism for generating initial data for binary black hole simulations, using a helical symmetry and Kerr-Schild metrics to improve accuracy and applicability for dynamical evolutions.

Contribution

The authors develop a novel approach combining helical symmetry and Kerr-Schild backgrounds for more realistic binary black hole initial data in numerical relativity.

Findings

Successfully constructed quasi-equilibrium initial data for binary black holes.

Improved initial data accuracy over conformally flat models.

Generated a preliminary inspiral sequence for binary black holes.

Abstract

We present a formalism for constructing quasi-equilibrium binary black hole initial data suitable for numerical evolution. We construct quasi-equilibrium models by imposing an approximate helical Killing symmetry appropriate for quasi-circular orbits. We use the sum of two Kerr-Schild metrics as our background metric, thereby improving on conformally flat backgrounds that do not accommodate rotating black holes and providing a horizon-penetrating lapse, convenient for implementing black hole excision. We set inner boundary conditions at an excision radius well inside the apparent horizon and construct these boundary conditions to incorporate the quasi-equilibrium condition and recover the solution for isolated black holes in the limit of large separation. We use our formalism both to generate initial data for binary black hole evolutions and to construct a crude quasi-equilibrium, inspiral sequence for binary black holes of fixed irreducible mass.