The gravitational S-matrix

TL;DR

This paper explores the theoretical properties and potential existence of a gravitational S-matrix, analyzing its behavior across different regimes and discussing implications for unitarity, causality, and nonlocality in quantum gravity.

Contribution

It provides a detailed analysis of the expected properties and regimes of a gravitational S-matrix, including its analytic structure and implications for nonlocality and black hole formation.

Findings

Distinct scattering behaviors in different gravity regimes

Constraints on amplitude behavior from crossing and causality

Proposal of nonlocality consistent with fundamental principles

Abstract

We investigate the hypothesized existence of an S-matrix for gravity, and some of its expected general properties. We first discuss basic questions regarding existence of such a matrix, including those of infrared divergences and description of asymptotic states. Distinct scattering behavior occurs in the Born, eikonal, and strong gravity regimes, and we describe aspects of both the partial wave and momentum space amplitudes, and their analytic properties, from these regimes. Classically the strong gravity region would be dominated by formation of black holes, and we assume its unitary quantum dynamics is described by corresponding resonances. Masslessness limits some powerful methods and results that apply to massive theories, though a continuation path implying crossing symmetry plausibly still exists. Physical properties of gravity suggest nonpolynomial amplitudes, although crossing and causality constrain (with modest assumptions) this nonpolynomial behavior, particularly requiring a polynomial bound in complex s at fixed physical momentum transfer. We explore the hypothesis that such behavior corresponds to a nonlocality intrinsic to gravity, but consistent with unitarity, analyticity, crossing, and causality.