Radiated Angular Momentum and Dissipative Effects in Classical Scattering

TL;DR

This paper derives a new formula for the angular momentum radiated in gravitational scattering, completing the set of Poincare charges, and computes these effects to third order in G using amplitude and effective field theory methods.

Contribution

It introduces a novel formula for radiated angular momentum, relates it to known linear momentum formulas, and calculates these quantities to third order in G for scattering of spinless particles.

Findings

Derived exact relations for radiated angular momentum and linear momentum.

Calculated radiated angular momentum to third order in G for spinless particle scattering.

Identified a new relation between energy and angular momentum loss at third order.

Abstract

We present a new formula for the angular momentum $J^{\mu\nu}$ carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum $P^\mu$, completes the set of radiated Poincare charges due to scattering. We parametrize $P^\mu$ and $J^{\mu\nu}$ by non-perturbative form factors and derive exact relations using the Poincare algebra. There is a contribution to $J^{\mu\nu}$ due to static (zero-frequency) modes, which can be derived from Weinberg's soft theorem. Using tools from scattering amplitudes and effective field theory, we calculate the radiated $J^{\mu\nu}$ due to the scattering of two spinless particles to third order in Newton's constant $G$, but to all orders in velocity. Our form-factor analysis elucidates a novel relation found by Bini, Damour, and Geralico between energy and angular momentum loss at $\mathcal{O}(G^3)$. Our new results have several nontrivial implications for binary scattering at $\mathcal{O}(G^4)$. We give a procedure to bootstrap an effective radiation reaction force from the loss of Poincare charges due to scattering.