Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

Abstract

The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity waveextraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at J + . However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.

Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

“…In Refs. [31,48], it was found that differences between extrapolated and CCE quantities were on the order of the discretization error of the Cauchy simulation. Additionally, the differences were found to be non-convergent, suggesting that the waveform extraction error could become dominant for high-accuracy simulations.…”

General relativistic null-cone evolutions with a high-order scheme

“…This is important for future application in onthe-fly Cauchy-characteristic extraction, where the metric data will be transported to J + during Cauchy evolution without the need of an additional post-processing step (which is currently the case for the algorithm presented in [2,3]). Furthermore, this is necessary for a future implementation of Cauchy characteristic matching [33,7] in which the characteristic evolution is used to provide on-the-fly boundary data for a Cauchy evolution.…”

“…Most recently, they have been employed for the practical problem of measuring gravitational waves in a gauge-invariant and unambiguous way from numerically evolved spacetimes of binary black hole mergers [1,2,3,4], rotating stellar core collapse [5], and collapsar formation [6]. The technique, called Cauchycharacteristic extraction (CCE) (see [7] for a review) takes metric boundary data produced by a 3+1 evolution on a worldtube Γ of finite radius, and uses null-cone evolutions of the Einstein equations to transport that metric data to future null infinity, J + , the conformal outer boundary of spacetime where gravitational radiation is invariantly defined and interpreted in the Bondi gauge [8,9,10].…”

“…The technique, called Cauchycharacteristic extraction (CCE) (see [7] for a review) takes metric boundary data produced by a 3+1 evolution on a worldtube Γ of finite radius, and uses null-cone evolutions of the Einstein equations to transport that metric data to future null infinity, J + , the conformal outer boundary of spacetime where gravitational radiation is invariantly defined and interpreted in the Bondi gauge [8,9,10]. Thus, this technique removes the influence of near-zone and coordinate effects [1,2,3,4,5].…”

“…A prominent result was the first stable dynamical evolution of a black hole spacetime in three spatial dimensions achieved by the Pittsburgh group [11,12]. Since then, the Pittsburgh null code (or PITTNullCode) has become the main building block for current implementations of characteristic extraction used in numerical relativity simulations [1,2,3,4,5], and is now part of the publicly available Einstein Toolkit [13]. The code employs a single-null coordinate system, and is formulated in terms of spin-weighted variables that are related to the original variables defined by Bondi and collaborators [8,9,10].…”