Approximate initial data for binary black holes

TL;DR

This paper presents an analytical method to generate initial data for binary black hole systems in quasicircular orbits, using perturbations of Schwarzschild solutions and the puncture method, accurate to first order in separation and momentum.

Contribution

It introduces a fully analytic approach to approximate initial data for binary black holes, improving computational efficiency and understanding of initial conditions.

Findings

Provides explicit analytic initial data for binary black holes

Achieves accuracy to first order in inverse separation and momentum

Facilitates faster initial data generation for simulations

Abstract

We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the transverse-traceless decomposition and consider perturbations of Schwarzschild black holes caused by boosts and the presence of a binary companion. A superposition of these two perturbations then yields approximate, but fully analytic binary black hole initial data that are accurate to first order in the inverse of the binary separation and the square of the black holes' momenta.