Measuring eccentricity in binary black-hole initial data

TL;DR

This paper introduces methods to measure and calibrate the eccentricity of initial data for binary black-hole systems, enhancing the understanding of their physical configurations and improving initial data construction techniques.

Contribution

It presents a novel application of effective-potential techniques and proposes the Komar-mass difference as an invariant measure of orbital eccentricity.

Findings

Effective-potential techniques can calibrate eccentric initial data.

Post-Newtonian diagnostics help measure orbital eccentricity.

Komar-mass difference serves as an invariant eccentricity parameter.

Abstract

Initial data for evolving black-hole binaries can be constructed via many techniques, and can represent a wide range of physical scenarios. However, because of the way that different schemes parameterize the physical aspects of a configuration, it is not alway clear what a given set of initial data actually represents. This is especially important for quasiequilibrium data constructed using the conformal thin-sandwich approach. Most initial-data studies have focused on identifying data sets that represent binaries in quasi-circular orbits. In this paper, we consider initial-data sets representing equal-mass black holes binaries in eccentric orbits. We will show that effective-potential techniques can be used to calibrate initial data for black-hole binaries in eccentric orbits. We will also examine several different approaches, including post-Newtonian diagnostics, for measuring the eccentricity of an orbit. Finally, we propose the use of the ``Komar-mass difference'' as a useful, invariant means of parameterizing the eccentricity of relativistic orbits.