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arXiv · 2203.04283

Radiated Angular Momentum and Dissipative Effects in Classical Scattering

Aneesh V. Manohar·Alexander K. Ridgway·Chia-Hsien Shen
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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.

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Aneesh V. Manohar, Alexander K. Ridgway, Chia-Hsien Shen. 2022-03-08. Radiated Angular Momentum and Dissipative Effects in Classical Scattering. https://doi.org/10.1103/physrevlett.129.121601

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