Gauge conditions for binary black hole puncture data based on an approximate helical Killing vector

TL;DR

This paper demonstrates a gauge choice for binary black hole puncture data that approximates a helical Killing vector, improving the understanding of initial data conditions for binary black hole simulations.

Contribution

It introduces a gauge condition that aligns puncture data with an approximate helical Killing vector, satisfying mass conditions and reducing evolution timescales.

Findings

Komar and ADM mass agree at spatial infinity.

3-metric evolves on a timescale smaller than the orbital period.

Extrinsic curvature time derivative remains significant.

Abstract

We show that puncture data for quasicircular binary black hole orbits allow a special gauge choice that realizes some of the necessary conditions for the existence of an approximate helical Killing vector field. Introducing free parameters for the lapse at the punctures we can satisfy the condition that the Komar and ADM mass agree at spatial infinity. Several other conditions for an approximate Killing vector are then automatically satisfied, and the 3-metric evolves on a timescale smaller than the orbital timescale. The time derivative of the extrinsic curvature however remains significant. Nevertheless, quasicircular puncture data are not as far from possessing a helical Killing vector as one might have expected.