Momentum flow in black-hole binaries: II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins

TL;DR

This paper uses numerical simulations to study momentum transfer and horizon dynamics during head-on mergers of equal-mass black holes with antiparallel spins, revealing insights into nonlinear spacetime behavior.

Contribution

It introduces a novel numerical approach to analyze momentum flow and horizon velocities in black-hole mergers using the Landau-Lifshitz formulation, comparing different gauges and with post-Newtonian results.

Findings

Horizon effective velocities closely match coordinate velocities.

Good agreement between pseudospectral and moving-puncture simulations.

Consistent results when comparing with post-Newtonian trajectories.

Abstract

Research on extracting science from binary-black-hole (BBH) simulations has often adopted a "scattering matrix" perspective: given the binary's initial parameters, what are the final hole's parameters and the emitted gravitational waveform? In contrast, we are using BBH simulations to explore the nonlinear dynamics of curved spacetime. Focusing on the head-on plunge, merger, and ringdown of a BBH with transverse, antiparallel spins, we explore numerically the momentum flow between the holes and the surrounding spacetime. We use the Landau-Lifshitz field-theory-in-flat-spacetime formulation of general relativity to define and compute the density of field energy and field momentum outside horizons and the energy and momentum contained within horizons, and we define the effective velocity of each apparent and event horizon as the ratio of its enclosed momentum to its enclosed mass-energy. We find surprisingly good agreement between the horizons' effective and coordinate velocities. To investigate the gauge dependence of our results, we compare pseudospectral and moving-puncture evolutions of physically similar initial data; although spectral and puncture simulations use different gauge conditions, we find remarkably good agreement for our results in these two cases. We also compare our simulations with the post-Newtonian trajectories and near-field energy-momentum. [Abstract abbreviated; full abstract also mentions additional results.]