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2022

Angular momentum of zero-frequency gravitons

Di Vecchia, Paolo, Heissenberg, Carlo, Russo, Rodolfo

Understand

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.