The gravitational eikonal: from particle, string and brane collisions to black-hole encounters

TL;DR

This paper reviews the gravitational eikonal approach, a method for calculating classical gravitational observables in high-energy collisions involving particles, strings, and branes, especially in black-hole encounters, complementing traditional techniques.

Contribution

It provides a comprehensive summary of the gravitational eikonal formalism and recent developments, particularly for massive scalars coupled to gravity, in the context of black-hole physics.

Findings

Eikonal exponentiation aids in calculating classical gravitational observables.

The approach complements Post-Newtonian, worldline, and Effective-One-Body methods.

Recent focus on black-hole encounters enhances understanding of gravitational wave sources.

Abstract

Motivated by conceptual problems in quantum theories of gravity, the gravitational eikonal approach, inspired by its electromagnetic predecessor, has been successfully applied to the transplanckian energy collisions of elementary particles and strings since the late eighties, and to string-brane collisions in the past decade. After the direct detection of gravitational waves from black-hole mergers, most of the attention has shifted towards adapting these methods to the physics of black-hole encounters. For such systems, the eikonal exponentiation provides an amplitude-based approach to calculate classical gravitational observables, thus complementing more traditional analytic methods such as the Post-Newtonian expansion, the worldline formalism, or the Effective-One-Body approach. In this review we summarize the main ideas and techniques behind the gravitational eikonal formalism. We discuss how it can be applied in various different physical setups involving particles, strings and branes and then we mainly concentrate on the most recent developments, focusing on massive scalars minimally coupled to gravity, for which we aim at being as self-contained and comprehensive as possible.