Unambiguous Determination of Gravitational Waveforms from Binary Black Hole Mergers

Abstract

Gravitational radiation is properly defined only at future null infinity (J þ ), but in practice it is estimated from data calculated at a finite radius. We have used characteristic extraction to calculate gravitational radiation at J þ for the inspiral and merger of two equal-mass nonspinning black holes. Thus we have determined the first unambiguous merger waveforms for this problem. The implementation is general purpose and can be applied to calculate the gravitational radiation, at J þ , given data at a finite radius calculated in another computation.

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.…”

“…This technique has been used in Refs. [31][32][33] for simulations of binary black hole mergers and in Refs. [34][35][36][37] for simulations of stellar collapse, binary neutron star mergers, and black hole formation.…”

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

“…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].…”