Conformally curved binary black hole initial data including tidal deformations and outgoing radiation

TL;DR

This paper presents a method for generating initial data for nonspinning black hole binaries that includes tidal deformations and outgoing radiation, aiming to reduce unphysical artifacts in simulations.

Contribution

The authors develop a conformally curved initial data set by matching post-Newtonian and tidally perturbed Schwarzschild metrics, improving realism over previous conformally flat models.

Findings

Data reduces initial spurious radiation in simulations.

Smooth interpolation minimizes additional constraint violations.

Uncontrolled remainders are estimated at O(v^5) and O(v^6).

Abstract

(Abridged) By asymptotically matching a post-Newtonian (PN) metric to two tidally perturbed Schwarzschild metrics, we generate approximate initial data (in the form of a 4-metric) for a nonspinning black hole binary in a circular orbit. We carry out this matching through O(v^4) in the binary's orbital velocity v, so the resulting data are conformally curved. Far from the holes, we use the appropriate PN metric that accounts for retardation, which we construct using the highest-order PN expressions available to compute the binary's past history. The data set's uncontrolled remainders are thus O(v^5) throughout the timeslice; we also generate an extension to the data set that has uncontrolled remainders of O(v^6) in the purely PN portion of the timeslice (i.e., not too close to the holes). The resulting data are smooth, since we join all the metrics together by smoothly interpolating between them. We perform this interpolation using transition functions constructed to avoid introducing excessive additional constraint violations. Due to their inclusion of tidal deformations and outgoing radiation, these data should substantially reduce the initial spurious ("junk") radiation observed in current simulations that use conformally flat initial data. Such reductions in the nonphysical components of the initial data will be necessary for simulations to achieve the accuracy required to supply Advanced LIGO and LISA with the templates necessary for parameter estimation.