Black-hole scattering with general spin directions from minimal-coupling amplitudes

Alfredo Guevara,Justin Vines,Alexander Ochirov

doi:10.1103/physrevd.100.104024

Abstract

We study the link between classical scattering of spinning black holes and quantum amplitudes for massive spin-$s$ particles. Generic spin orientations of the black holes are considered, allowing their spins to be deflected on par with their momenta. We rederive the spin-exponentiated structure of the relevant tree-level amplitude from minimal coupling to Einstein's gravity, which in the $s\to\infty$ limit generates the black holes' complete series of spin-induced multipoles. The resulting scattering function is seen to encode in a simple way the known net changes in the black-hole momenta and spins at first post-Minkowskian order. We connect our findings to a rigorous framework developed elsewhere for computing such observables from amplitudes.

Highlights

Applying techniques from quantum field theory to the study of the classical two-body problem in general relativity (GR) has produced significant progress in the treatment of the post-Newtonian (PN) approximation [1,2,3,4,5,6], expanding in small speeds and weak fields
We study the link between classical scattering of spinning black holes and quantum amplitudes for massive spin-s particles
We rederive the spin-exponentiated structure of the relevant treelevel amplitude from minimal coupling to Einstein’s gravity, which in the s → ∞ limit generates the black holes’ complete series of spin-induced multipoles

Summary

INTRODUCTION

Applying techniques from quantum field theory to the study of the classical two-body problem in general relativity (GR) has produced significant progress in the treatment of the post-Newtonian (PN) approximation [1,2,3,4,5,6], expanding in small speeds and weak fields. [26] from amplitudes, exploiting and further substantiating the remarkable fact that the BH multipole structure up to the 22s-pole level is reproduced by considering spin-s particles which are minimally coupled to gravity. [35] to compute the net changes in the momenta and spins for two-body scattering at 1PM order, reproducing the results for BHs up to quadrupolar order from minimally coupled spin-1 particles We extend such calculation to arbitrary spins s, and in the limit s → ∞ obtain all orders in the BH multipole expansions at 1PM order [26]

MINIMAL COUPLING TO GRAVITY

GENERAL INTEGER-SPIN SETUP

FOUR-POINT AMPLITUDE

LINEAR AND ANGULAR IMPULSES

SUMMARY AND DISCUSSION