High energy gravitational scattering: a numerical study

TL;DR

The paper investigates high-energy gravitational scattering using the ACV effective action, solving for the elastic S-matrix in a dipole-like two-body setup as the parameter $R$ approaches a critical value $R_{\rm crit}$. By iterative lattice methods and spectral analyses, it reveals a genuine transition at $R_{\rm crit}$ with observables displaying square-root scaling and a diverging perturbative expansion, while validating the approach against the axially symmetric case that reproduces known results. The main contributions include a precise determination of $R_{\rm crit}$ for dipole and axial configurations, a demonstration of universal square-root critical behavior in spectral and action-related quantities, and a clear demonstration that the transition is accompanied by an instability in the linearized operator. This work clarifies the nonperturbative regime of gravitational scattering, highlights the role of cutoff dependencies, and lays groundwork for incorporating rescattering and infrared effects in future studies.

Abstract

The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action introduced by Amati, Ciafaloni and Veneziano we find that the perturbative expansion around the leading eikonal result diverges at a critical value signalling the onset of a new regime. We then discuss the main features of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact parameter. The nature of the singularity is studied with particular attention to the scaling behaviour of various observables at the transition. The numerical approach is validated by reproducing the known exact solution in the axially symmetric case to high accuracy.