Planckian Energy Scattering and Surface Terms in the Gravitational Action

TL;DR

This paper introduces a novel approach to Planckian-energy gravitational scattering, expressing the S-matrix phase through surface and boundary terms in the gravitational action, and validates it against known strong-field scattering cases.

Contribution

It presents a new method linking the scattering phase to surface and boundary terms in the gravitational action, applicable at all orders in the ratio R/b.

Findings

Validates the approach at leading order in R/b

Matches known results in strong gravitational fields

Provides a framework for analyzing high-energy gravitational scattering

Abstract

This is a revised version of our previous paper by the same name and preprint number. It contains various changes, two figures and new results in sect.5. We propose a new approach to four-dimensional Planckian-energy scattering in which the phase of the ${\cal S}$-matrix is written---to leading order in $\hbar$ and to all orders in $R/b =Gs/J$---in terms of the surface term of the gravity action and of a boundary term for the colliding quanta. The proposal is checked at the leading order in $R/b$ and also against some known examples of scattering in strong gravitational fields.