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Radiated Angular Momentum and Dissipative Effects in Classical Scattering

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arxiv 2203.04283 v2 pith:EST3X5DN submitted 2022-03-08 hep-th gr-qc

classification hep-thgr-qc
keywords scatteringmomentumradiatedangularpoincarechargesclassicaleffective
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 8 Pith papers

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