Improved methods for simulating nearly extremal binary black holes

TL;DR

This paper introduces improved numerical methods for simulating nearly extremal binary black holes, enabling more robust and efficient gravitational wave predictions for highly spinning black hole mergers.

Contribution

The authors develop and demonstrate new techniques that allow stable and efficient simulations of nearly extremal black hole binaries with spins exceeding previous limits.

Findings

Successful simulation of a binary with black hole spin S/m^2=0.99

Simulation of nearly extremal binary with S/m^2=0.994 for both black holes

Comparison of numerical waveforms with post-Newtonian and effective-one-body models

Abstract

Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass $m$ and spin $S$ exceeding the Bowen-York limit of $S/m^2=0.93$. We present improved methods that enable us to simulate merging, nearly extremal black holes more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole coalescence, where the larger black hole has $S/m^2=0.99$. We also use these methods to simulate a non-precessing binary black hole coalescence, where both black holes have $S/m^2=0.994$, nearly reaching the Novikov-Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black-hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called "orbital hangup" effect).