Test black holes, scattering amplitudes and perturbations of Kerr spacetime

TL;DR

This paper tests theoretical predictions relating scattering amplitudes of spinning black holes to perturbations of Kerr spacetime, confirming some conjectures about the conservative dynamics of aligned-spin binary black holes at high post-Newtonian orders.

Contribution

It provides the first non-perturbative verification of amplitude-based predictions for black hole scattering using Kerr spacetime perturbations.

Findings

Confirmed conjectures about spin-dependent parts of binary black hole dynamics.

Validated the kinematical mapping between test and comparable-mass black hole scattering.

Extended the understanding of black hole interactions beyond previous perturbative orders.

Abstract

It has been suggested that amplitudes for quantum higher-spin massive particles exchanging gravitons lead, via a classical limit, to results for scattering of spinning black holes in general relativity, when the massive particles are in a certain way minimally coupled to gravity. Such limits of such amplitudes suggest, at least at lower orders in spin, up to second order in the gravitational constant $G$, that the classical aligned-spin scattering function for an arbitrary-mass-ratio two-spinning-black-hole system can be obtained by a simple kinematical mapping from that for a spinning test black hole scattering off a stationary background Kerr black hole. Here we test these suggestions, at orders beyond the reach of the post-Newtonian and post-Minkowskian results used in their initial partial verifications, by confronting them with results from general-relativistic "self-force" calculations of the linear perturbations of a Kerr spacetime sourced by a small orbiting body, here considering only results for circular orbits in the equatorial plane. We translate between scattering and circular-orbit results by assuming the existence of a local-in-time canonical Hamiltonian governing the conservative dynamics of generic (bound and unbound) aligned-spin orbits, while employing the associated first law of spinning binary mechanics. We confirm, through linear order in the mass ratio, some previous conjectures which would begin to fill in the spin-dependent parts of the conservative dynamics for arbitrary-mass-ratio aligned-spin binary black holes at the fourth-and-a-half and fifth post-Newtonian orders.