Binary black hole evolutions of approximate puncture initial data

TL;DR

This study evaluates the accuracy of approximate puncture initial data based on skeleton solutions in binary black hole simulations, showing high waveform agreement and analyzing constraint violations and their evolution.

Contribution

It demonstrates that skeleton initial data can produce waveforms closely matching constraint-satisfying data, with quantification of constraint violations and their decay during evolution.

Findings

Waveform matches exceed 0.97 for total mass > 40 solar masses.

Skeleton data initially violate Hamiltonian constraints near punctures.

Constraint violations decay over time, leading to a relaxed, accurate evolution.

Abstract

Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that evaluates the effects that approximate puncture initial data, based on "skeleton" solutions to the Einstein constraints as proposed by Faye et al. [PRD 69, 124029 (2004)], have on numerical evolutions. Using data analysis tools, we assess the effectiveness of these constraint-violating initial data and show that the matches of waveforms from skeleton data with the corresponding waveforms from constraint-satisfying initial data are > 0.97 when the total mass of the binary is > 40M(solar). In addition, we demonstrate that the differences between the skeleton and the constraint-satisfying initial data evolutions, and thus waveforms, are due to negative Hamiltonian constraint violations present in the skeleton initial data located in the vicinity of the punctures. During the evolution, the skeleton data develops both Hamiltonian and momentum constraint violations that decay with time, with the binary system relaxing to a constraint-satisfying solution with black holes of smaller mass and thus different dynamics.