A Phase Space for Gravitational Radiation

TL;DR

This paper introduces a rigorous new framework for the phase space of gravitational radiation in General Relativity, clarifying its structure, symplectic form, and relation to infrared sectors and symmetries.

Contribution

It provides a novel, well-posed definition of the gravitational radiation phase space, including its fiber structure, symplectic form, and the role of supertranslations.

Findings

Defined the phase space for gravitational radiation

Identified the symplectic form rigorously

Connected infrared sectors to supertranslation actions

Abstract

We give a new definition, based on considerations of well-posedness for a certain asymptotic initial value problem, of the phase space for the radiative degrees of freedom of the gravitational field in exact General Relativity. This space fibres over the space of final states, with the fibres being the purely radiative degrees of freedom. The symplectic form is rigorously identified. The infrared sectors are shown to be the level surfaces of a moment map of an action of the quotient group Supertranslations/Translations. A similar result holds for Electromagnetism in Minkowski space.