Gravitational Self Force from Scattering Amplitudes in Curved Space

TL;DR

This paper uses scattering amplitudes in curved spacetime to model gravitational self-force effects on a particle orbiting a massive body, enabling precise calculations relevant for gravitational wave astronomy.

Contribution

It introduces a novel approach employing curved space amplitudes to compute self-force effects, including backreaction, to all orders in gravitational constant G.

Findings

Verified geodesic motion in Schwarzschild background

Calculated first-order self-force correction to two-body scattering

Demonstrated advantages of curved space amplitudes for gravitational wave modeling

Abstract

We employ scattering amplitudes in curved space to model the dynamics of a light probe particle with mass $m$ orbiting in the background spacetime induced by a heavy gravitational source with mass $M$. Observables are organized as an expansion in $m/M$ to all orders in $G$ -- the gravitational self-force expansion. An essential component of our analysis is the backreaction of the heavy source which we capture by including the associated light degrees of freedom. As illustration we consider a Schwarzschild background and verify geodesic motion as well as the first-order self-force correction to two-body scattering through ${\cal O}(G^3)$. Amplitudes in curved space offer several advantages, and further developments along these lines may advance the computation of gravitational-wave signals for extreme-mass-ratio inspirals.