The SAGEX Review on Scattering Amplitudes, Chapter 13: Post-Minkowskian expansion from Scattering Amplitudes

Abstract

The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context. In this brief review, we focus on the post-Minkowskian expansion as applied to the two-body problem in general relativity without spin, and we describe how relativistic quantum field theory can be used to greatly simplify analytical calculations based on the Einstein-Hilbert action. Subtleties related to the extraction of classical physics from such quantum mechanical calculations highlight the care which must be taken when both positive and negative powers of Planck's constant are at play. In the process of obtaining classical results in both Einstein gravity and supergravity, one learns new aspects of quantum field theory that are obscured when using units in which Planck's constant is set to unity. The scattering amplitude approach provides a self-contained framework for deriving the two-body scattering valid in all regimes of energy. There is hope that the full impact of amplitude computations in this field may significantly alter the way in which gravitational wave predictions will advance in the coming years.

The SAGEX review on scattering amplitudes*

“…2.13. Post-Minkowskian expansion from scattering amplitudes [13] The post-Minkowskian expansion in general relativity is based on expanding observable quantities in Newton's constant G N only. Measuring physical quantities at infinity where space-time is Minkowskian, this corresponds to an expansion in gravity that is special relativistic (valid to all orders in velocities) and without the imposition of the counting based upon the virial theorem for bound orbits.…”

The SAGEX review on scattering amplitudes Chapter 1: Modern fundamentals of amplitudes

“…21 We also mention important applications of unitarity to the study of black hole scattering in general relativity [130][131][132][133][134][135][136][137][138][139][140][141][142][143][144], and in theories of modified gravity with higher-derivative interactions [145][146][147][148][149]. See chapters 13 and 14 of this review [150,151] for more details.…”

“…Hence the integrand thus produced must be part of the complete answer, and by going through all kinematic channels we have enough constraints to fix the integrand for the amplitude. The key advantage is that we can simplify the cut integrand (150) as much as possible using on-shell conditions and powerful spinor-helicity techniques before lifting it back to a full Feynman loop integrand (151). Once we have combined the information from all cuts, we can PV-reduce the resulting integrand (which is an algebraic process) and read off the coefficients a i , b j and c k .…”

The SAGEX review on scattering amplitudes Chapter 14: Classical gravity from scattering amplitudes

“…This review is one of a series describing the current status of research in scattering amplitudes and their applications; see reference [105] for the overview article. Two chapters in this series are closely related to ours: reference [106], which reviews the double copy of scattering amplitudes and their applications, and contains a section on classical gravity; and reference [107], which is dedicated to the applications of amplitudes in classical gravity, via different approaches to the one we review here.…”