Radiated Angular Momentum and Dissipative Effects in Classical Scattering

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.

5 pages +refs, two figures and one Mathematica ancillary file for table I; minor revision and fixed a typo in the definition of Δb, matched to PRL version in v2

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