The Lazarus Project. II. Spacelike extraction with the quasi-Kinnersley tetrad

TL;DR

The Lazarus project combines short, fully nonlinear 3D simulations with Kerr-based perturbation theory to recover gravitational-wave content from black-hole mergers. This work advances the method by introducing a quasi-Kinnersley frame, a locally defined transverse tetrad that approaches the Kinnersley tetrad up to a spin-boost, thereby reducing ad hoc coordinate and tetrad corrections in wave extraction. The authors implement a tetrad-reconstruction procedure based on Weyl-tensor eigenvectors, test it on spinning Bowen-York, Brill-Lindquist head-on, and QC0 data, and show improved consistency and a clearer error budget for the tetrad dependence while highlighting limitations from the underlying ADM evolution. The approach enables earlier and more robust Teukolsky-based wave extraction, provides a path toward direct near-field radiation interpretation, and sets the stage for longer, more accurate evolutions with modern numerical-relativity frameworks such as LazEv.

Abstract

The Lazarus project was designed to make the most of limited 3D binary black-hole simulations, through the identification of perturbations at late times, and subsequent evolution of the Weyl scalar $Ψ_4$ via the Teukolsky formulation. Here we report on new developments, employing the concept of the ``quasi-Kinnersley'' (transverse) frame, valid in the full nonlinear regime, to analyze late-time numerical spacetimes that should differ only slightly from Kerr. This allows us to extract the essential information about the background Kerr solution, and through this, to identify the radiation present. We explicitly test this procedure with full numerical evolutions of Bowen-York data for single spinning black holes, head-on and orbiting black holes near the ISCO regime. These techniques can be compared with previous Lazarus results, providing a measure of the numerical-tetrad errors intrinsic to the method, and give as a by-product a more robust wave extraction method for numerical relativity.

Figures (10)

• Figure 1: The real part of the $\mathcal{S}$ invariant along the $x$ axis for Spinning BY data, at different extraction times $T$.
• Figure 2: Total radiated energy for Spinning BY data as calculated from original (L1) and new (L2) Lazarus methods, as a function of extraction time $T$.
• Figure 3: Evolution of the $m=0$ Spinning BY waveform for the new (L2) Lazarus method, evaluated at $r_* = 30\,M$ along maximal amplitude directions: $\theta = 90^\circ$ for $Re(\Psi_4)$, $\theta = 45^\circ$ for $Im(\Psi_4)$. The five curves represent five different extraction times in the energy plateau of Fig. \ref{['fig:BY-EvsT']}.
• Figure 4: The $\mathcal{S}$ invariant along the $z$ axis for Head-On data, at different extraction times $T$.
• Figure 5: Radiated energy for Head-On collision as calculated from original (L1) and new (L2) Lazarus methods, as a function of extraction time $T$. Note the extension of the plateau with increasing resolution.