Revisiting gravitational angular momentum and mass dipole losses in the eikonal framework

TL;DR

This paper reviews gravitational scattering of compact objects using the eikonal framework, combining post-Minkowskian and post-Newtonian methods to analyze angular momentum and mass dipole losses with implications for gravitational-wave signals.

Contribution

It integrates next-to-leading PM waveforms with static losses to accurately compute angular momentum and mass dipole changes, highlighting subtleties in their physical interpretation.

Findings

Reproduces known angular momentum loss results up to 4PM and 2.5PN order.

Provides new expressions for mass dipole change considering nonlinear memory.

Discusses the sensitivity of mass dipole to Coulombic and memory effects.

Abstract

We review the description of classical gravitational scatterings of two compact objects by means of the eikonal framework. This encodes via scattering amplitudes both the motion of the bodies and the gravitational-wave signals that such systems produce. As an application, we combine the next-to-leading post-Minkowskian (PM) waveform derived in the post-Newtonian (PN) limit with the 4PM static loss due to the linear memory effect to reproduce known results for the total angular mometum loss in the center-of-mass frame up to $\mathcal O(G^4)$ and 2.5PN order. We also provide similar expressions for the change in the system's mass dipole, discussing the subtleties related to its sensitivity to the Coulombic components of the field and to the nonlinear memory effect.