Asymptotically Matched Spacetime Metric for Non-Precessing, Spinning Black Hole Binaries

Abstract

We construct a closed-form, fully analytical 4-metric that approximately represents the spacetime evolution of non-precessing, spinning black hole binaries from infinite separations up to a few orbits prior to merger. We employ the technique of asymptotic matching to join a perturbed Kerr metric in the neighborhood of each spinning black hole to a near-zone, post-Newtonian metric farther out. The latter is already naturally matched to a far-zone, post-Minkowskian metric that accounts for full temporal retardation. The result is a 4-metric that is approximately valid everywhere in space and in a small bundle of spatial hypersurfaces. We here restrict our attention to quasi- circular orbits, but the method is valid for any orbital motion or physical scenario, provided an overlapping region of validity or buffer zone exists. A simple extension of such a metric will allow for future studies of the accretion disk and jet dynamics around spinning back hole binaries.

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• Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling
• Relativistic Dynamics and Mass Exchange in Binary Black Hole Mini-Disks
• Astrophysics of Super-massive Black Hole Mergers
• Circumbinary Disk Accretion into Spinning Black Hole Binaries
• Superposed metric for spinning black hole binaries approaching merger
• Approximate black hole binary spacetime via asymptotic matching
• Octupolar invariants for compact binaries on quasi-circular orbits
• Inspiralling, Non-Precessing, Spinning Black Hole Binary Spacetime via Asymptotic Matching
• Including realistic tidal deformations in binary black-hole initial data
• Spinning, Precessing, Black Hole Binary Spacetime via Asymptotic Matching
• Eccentric Catastrophes & What To Do With Them
• Inspiraling black-hole binary spacetimes: Challenges in transitioning from analytical to numerical techniques
• Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars