Binary black-hole evolutions of excision and puncture data

TL;DR

The paper presents Lean, a flexible numerical-relativity code that evolves binary black holes using multiple initial-data types (Brill-Lindquist, Misner, Kerr-Schild) within the BSSN framework, leveraging dynamic mesh refinement and both excision and moving-puncture techniques. It demonstrates state-of-the-art inspiral-merger waveforms with convergent results and conducts a detailed comparison of head-on collisions across data types, quantifying how initial data and gauge choices affect waveforms and radiated energy. Key findings show close agreement between conformally flat data (BL and Misner) and notable but explainable differences for Kerr-Schild data due to spurious radiation and finite-radius extraction, underscoring the importance of constraint solving for KS data and the role of gauge dynamics. The work advances waveform-template development for gravitational-wave astronomy by clarifying accuracy budgets and guiding future improvements in initial-data construction and evolution schemes.

Abstract

We present a new numerical code developed for the evolution of binary black-hole spacetimes using different initial data and evolution techniques. The code is demonstrated to produce state-of-the-art simulations of orbiting and inspiralling black-hole binaries with convergent waveforms. We also present the first detailed study of the dependence of gravitational waveforms resulting from three-dimensional evolutions of different types of initial data. For this purpose we compare the waveforms generated by head-on collisions of superposed Kerr-Schild, Misner and Brill-Lindquist data over a wide range of initial separations.

Figures (13)

• Figure 1: Real part of the $\ell=2$, $m=2$ multipole of $Mr\Psi_4$ extracted from the $R1$ simulation at $r_{\rm ex}=60M$ obtained for resolutions $h_1$, $h_2$ and $h_3$.
• Figure 2: Convergence analysis of the $\ell=2$, $m=2$ multipole of $Mr\Psi_4$ without correcting the phase error (upper panel) and after applying a phase correction (lower panel).
• Figure 3: Convergence analysis of the Hamiltonian constraint on the $x$ axis at $t=128\,M$, shortly after the crossing of the punctures.
• Figure 4: Binding energy $E_b/M$ for Kerr-Schild (solid), Brill-Lindquist (short-dashed) and Misner (long-dashed) initial-data sets as function of the coordinate distance $D/M$ of the holes.
• Figure 5: Convergence analysis for the $\ell=2$, $m=0$ mode of the Newman-Penrose scalar $\Psi_4$ extracted at $r_{\rm ex}=40M$. The difference between the runs with higher resolutions has been amplified by a factor 1.58 expected for fourth-order convergence.