Improved Evolutions of Binary Black Hole Mergers with Slow-Start Lapse Gauge Condition using Z4c Formulation

Abstract

Interpreting gravitational wave (GW) signals from compact binary mergers hinges on the accuracy of numerical relativity (NR) simulations. With the proposed space-based Laser Interferometer Space Antenna (LISA) and other next-generation detectors on the horizon, there is a growing need for more accurate GW predictions as observational sensitivity pushes into more complex parameter regimes. In this work, we investigate the impact of the slow start lapse (SSL) gauge condition, proposed by Zachary Etienne, in moving-puncture simulations of binary black hole (BBH) mergers using the Z4c formulation to solve the Einstein field equations (EFEs). The SSL technique modifies the lapse evolution condition by introducing a damping term that delays the formation of the sharp lapse feature, which is responsible for significant numerical errors in BBH simulations. Using AthenaK—an open-source, performance-portable astrophysics code that leverages GPU computing—we simulate the evolutions of a single black hole (BH), a BBH head-on collision, and a quasicircular BBH system to assess the effects of SSL when paired with Z4c formulation. We also examine its impact on the performance of the apparent horizon (AH) finder AHFinderDirect in these cases. We find that SSL significantly reduces Hamiltonian and momentum-constraint violations—by up to two orders of magnitude in the wavezone—suppresses spurious early-time oscillations in the extracted GWs, and improves convergence behavior. Specifically, analysis of AHFinderDirect diagnostics shows that SSL ensures the continued convergence of the irreducible mass of the BHs as resolution increases. These results indicate that SSL offers meaningful improvements to the accuracy of puncture simulations with Z4c formulation, just as it does for those using the BSSN formulation as demonstrated by Etienne, thereby supporting the development of more precise waveform models for the next era of GW astronomy.