Asymptotic Simplicity and Scattering in General Relativity from Quantum Field Theory

TL;DR

This work investigates asymptotic simplicity and the peeling property in general relativity for relativistic two-body scattering by computing the finite-distance metric from the final-state graviton one-point function in momentum space. Using a KMOC-inspired, off-shell framework, it distinguishes radiation and Coulomb regions in the Fourier transform and shows that analytic contributions preserve Sachs's peeling, while nonanalytic, long-range effects—particularly at ${\cal O}(G^3)$—drive new, stronger peeling violations. The findings connect gravitational memory, soft theorems, and tail effects to the breakdown of peeling, with potential implications for asymptotic symmetries and the infrared structure of gravity. The methodology bridges quantum-field-theoretic techniques with classical gravitational observables, offering a pathway to test asymptotic properties of spacetime in physically realistic scattering processes.

Abstract

We investigate the fate of asymptotic simplicity in physically relevant settings of compact-object scattering. Using the stress tensor of a two-body system as a source, we compute the spacetime metric in General Relativity at finite observer distance in an asymptotic expansion. To do so, we relate the metric to the final-state graviton one-point function in momentum space, which is computed using perturbative QFT techniques. Both the simple pole and the infrared-related logarithmic branch cut in the virtuality of the external graviton contribute nontrivially. We focus on determining the fall-off behavior of the Newman-Penrose scalars, confirming previous predictions that Sachs's peeling property is violated at leading order in the post-Minkowski expansion. Our analysis at higher orders in the post-Minkowskian expansion reveals a significantly stronger breakdown of the peeling property than previously recognized, which is the result of nonlinear, long-range interactions between localized sources and the surrounding gravitational field.

Figures (5)

• Figure 1: Typical diagrams contributing to the final-state graviton one-point function in Eq. \ref{['eq:h']}.
• Figure 2: The contour deformation of the $z$-integral. The original contour, denoted in blue, is equal to the sum of the advanced and retarded contours, denoted in red. We focus on the advanced contour.
• Figure 3: At leading order, the current $J^{\mu\nu}(k)$ can be regarded to as an analytic function of $\omega$ and the integral over $\omega$ can be evaluated via residue theorem, on the poles introduced by the external (retarded) propagator. For $t >0$, we can smoothly deform the original contour (in red) into the two contours encircling such poles (in blue).
• Figure 4: At ${\cal O}(G^3)$ the current $J^{\mu\nu}(k)$ has logarithmic branch-cuts as a function of $\omega$. We deform the initial integration contour along the real axis to the two contours ${\cal C}_{1,2}$ around the branch cuts.
• Figure 5: We break up the integral over $\mathcal{C}_{1}$ into two parts, denoted in blue and green respectively. Both contours, integrated separately, are logarithmically divergent in $\rho$.