Self-force effects in post-Minkowskian scattering

TL;DR

This paper analytically computes self-force effects and explicit two-body scattering solutions at second post-Minkowskian order, clarifying their role in gravitational scattering and providing foundational results for future higher-order studies.

Contribution

It presents the first explicit second post-Minkowskian order solutions for two-body gravitational scattering, including self-force effects and conserved quantities, advancing understanding of PM scattering theory.

Findings

Calculated scalar, electromagnetic, and gravitational self-force on a particle at large distances.

Derived explicit two-body scattering trajectories at 2PM order.

Reproduced known momentum transfer and flux results, and identified new conserved quantities.

Abstract

We revisit the old problem of the self-force on a particle moving in a weak-field spacetime in the context of renewed interest in two-body gravitational scattering. We analytically calculate the scalar, electromagnetic, and gravitational self-force on a particle moving on a straight-line trajectory at a large distance from a Newtonian star, and use these results to find the associated correction to its motion. In the gravitational case we must also include the matter-mediated force, which acts at the same perturbative order as the gravitational self-force. We further augment the gravitational results with geodesic calculations at second order in the central body mass to determine the full, explicit solution to the two-body gravitational scattering problem at second post-Minkowskian order (2PM). We calculate the momentum transfer (which reproduces Westpfahl's old result), the change in mechanical angular momentum (which matches the radiative flux recently computed by Damour), and the change in mechanical mass moment (the time-space components of the angular momentum tensor), which has not previously appeared. Besides the new 2PM results of explicit trajectories and all conserved quantities, this work clarifies the role of gravitational self-force in PM scattering theory and provides a foundation for higher-order calculations.