Classical gravitational observables from the Eikonal operator

We propose two possible eikonal operators encoding the effects of classical radiation as coherent states of gravitons and show how to compute from them different classical observables. In the first proposal, only genuinely propagating gravitons are included, while, in the second, zero-frequency modes are added in order to recover the effects of a static gravitational field. We first calculate the radiated energy momentum and the change in each particle's momentum, or impulse, to 3PM order finding agreement with the literature. We then calculate the angular momentum of the gravitational field after the collision. In order to do so, we adapt the method of reverse unitarity to the presence of derivatives in the operators describing the angular momentum and reproduce the result of [1] obtained by resumming the small-velocity expansion. As a new application, we derive also the variation in each particle's angular momentum up to 3PM: calculating separately field and particle contributions allows us to check the balance laws explicitly. We also show how the eikonal operator encodes the linear-response formula of Bini-Damour by deriving the linear radiation-reaction contribution to the transverse impulse at 4PM.

Automated summary

In this paper, two possible eikonal operators encoding the effects of classical radiation as coherent states of gravitons are proposed, and it is shown how to compute different classical observables from them. The first proposal includes only genuinely propagating gravitons, while the second adds zero-frequency modes to recover the effects of a static gravitational field. The author calculated the radiated energy momentum and the change in each particle's momentum up to 3PM order, finding agreement with previous literature. The angular momentum of the gravitational field after the collision and the variation in each particle's angular momentum up to 3PM are also calculated, and the eikonal operator's encoding of the linear-response formula of Bini-Damour is derived.