Spinning, Precessing, Black Hole Binary Spacetime via Asymptotic Matching

TL;DR

This paper presents an analytic method to construct an approximate global spacetime for precessing, spinning binary black holes by matching solutions in different zones, capturing key relativistic effects.

Contribution

It introduces a novel asymptotic matching approach to combine Kerr, post-Newtonian, and post-Minkowskian metrics for precessing black hole binaries.

Findings

Constructed a global approximate spacetime for precessing binaries.

Successfully incorporated precession effects into the spacetime model.

Provides a framework for more accurate gravitational wave modeling.

Abstract

We briefly discuss a method to construct a global, analytic, approximate spacetime for precessing, spinning binary black holes. The spacetime construction is broken into three parts: the inner zones are the spacetimes close to each black hole, and are approximated by perturbed Kerr solutions; the near zone is far from the two black holes, and described by the post-Newtonian metric; and finally the wave (far) zone, where retardation effects need to be taken into account, is well modeled by the post-Minkowskian metric. These individual spacetimes are then stitched together using asymptotic matching techniques to obtain a global solution that approximately satisfies the Einstein field equations. Precession effects are introduced by rotating the black hole spin direction according to the precessing equations of motion, in a way that is consistent with the global spacetime construction.