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Radiated Angular Momentum and Dissipative Effects in Classical Scattering

Aneesh V Manohar¹, Alexander K Ridgway¹, Chia-Hsien Shen¹

¹Department of Physics 0319, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.

Physical Review Letters

|September 30, 2022

Abstract:

We present a new formula for the angular momentum J^{μν} carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum P^{μ}, completes the set of radiated Poincaré charges due to scattering. We parametrize P^{μ} and J^{μν} by nonperturbative form factors and derive exact relations using the Poincaré algebra. There is a contribution to J^{μν} 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^{μν} 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 O(G^{3}). Our new results have several nontrivial implications for binary scattering at O(G^{4}). We give a procedure to bootstrap an effective radiation reaction force from the loss of Poincaré charges due to scattering.

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