High energy gravitational scattering: a numerical study

TL;DR

This paper numerically investigates high energy gravitational scattering, revealing a divergence in the S-matrix at a critical impact parameter indicating a transition to a new regime associated with gravitational collapse.

Contribution

It introduces a numerical method to study the S-matrix in high energy gravitational scattering, identifying a critical impact parameter where classical collapse effects emerge.

Findings

Perturbative expansion diverges at a critical impact parameter.

The S-matrix becomes singular at impact parameter ~2.22 times the Schwarzschild radius.

Numerical validation reproduces known solutions with high accuracy.

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.