Approximate Solutions to the Binary Black Hole Initial Value Problem

TL;DR

This paper introduces approximate analytical solutions for the initial value problem of binary black holes, simplifying the setup for numerical simulations by avoiding complex elliptic equation solving.

Contribution

It provides new analytical initial data solutions for binary black holes with arbitrary momentum, easing numerical implementation compared to traditional methods.

Findings

Analytical solutions for Hamiltonian and momentum constraints.

Applicable to systems with arbitrary linear and angular momentum.

Simplifies initial data setup for numerical relativity simulations.

Abstract

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints.