Gravitational self force from scattering amplitudes in curved space

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 (G³). 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.