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Angular momentum of zero-frequency gravitons

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arxiv 2203.11915 v2 pith:GEK37N2G submitted 2022-03-22 hep-th gr-qc

classification hep-thgr-qc
keywords softangulargravitonmomentumomegaarbitrarycapturescontribution
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

By following closely Weinberg's soft theorem, which captures the $1/\omega$ pole contribution to the amplitude for soft graviton emissions ($\omega<\Lambda$) on top of an arbitrary background hard process, we calculate the expectation value of the graviton's angular momentum operator for arbitrary collisions dressed with soft radiation. We find that the result becomes independent of the cutoff $\Lambda$ on the graviton's frequency, effectively localizing at $\omega=0$. In this way, our result captures the contribution to the angular momentum that comes from the zero-frequency modes. Like the soft theorem, our formula has an exact dependence on the kinematics of the hard particles and is only a function of their momenta. As an example, we discuss in some detail the case of the $2 \to 2$ scattering of spinless particles in General Relativity and ${\cal N}=8$ supergravity.

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Cited by 4 Pith papers

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  4. Determination of the Angular Momentum of Radiated Gravitons, Scalars, and Dark Photons from Binary Orbits

    gr-qc 2026-08 conditional novelty 4.0 of 10

    Each radiated graviton from a binary carries about 2ħ of angular momentum and each scalar or vector quantum about ħ, with the graviton result extended from elliptical to hyperbolic orbits.

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