A Runway to Dissipation of Angular Momentum via Worldline Quantum Field Theory

TL;DR

This paper develops a diagrammatic worldline quantum field theory approach to compute angular momentum flux from black hole scattering, simplifying calculations and revealing dimension-dependent static contributions.

Contribution

It introduces static correlators and applies WQFT techniques to compute angular momentum flux, extending the formalism to include static contributions and higher-order effects.

Findings

Computed the $ ext{O}(G^3)$ angular momentum flux matching known results.

Revealed static contributions vanish in dimensions greater than four.

Extended the method to electromagnetic analogs at $ ext{O}( ext{alpha}^3)$.

Abstract

We extend the worldline quantum field theory formalism to include a direct diagrammatic method of computing the total flux of angular momentum from a black hole scattering event in the post-Minkowskian regime. Remarkably, except for subtle zero-frequency gravitons, the diagrammatic and integrational challenge is in a one-to-one correspondence with the analogous calculation of the black hole impulses -- and the well-developed WQFT methodologies for the impulse may thus be directly imported to this problem. Zero-frequency gravitons appear in this calculation as a "static" integration region in addition to the "dynamical" region usually encountered for the impulse. We show that a large class of static contributions can be organized systematically by introducing $n$-point functions referred to as "static correlators". They reduce to a simple one-loop integral family which we compute explicitly using integration-by-parts relations and the method of differential equations. In passing, our analysis shows that static contributions disappear in space-time dimensions $D>4$. As a concrete application of our new method, we compute explicitly the $\mathcal{O}(G^3)$ total flux of angular momentum reproducing known results. Further, we apply the same method to electromagnetism where we compute the analogous $\mathcal{O}(\alpha^3)$ result.