Asymptotic Structure with vanishing cosmological constant

TL;DR

This paper develops a new, easy-to-implement criterion for gravitational radiation in asymptotically flat space-times, based on tidal energies and Weyl curvature, providing a geometric reformulation of peeling behavior.

Contribution

It introduces a novel characterization of gravitational radiation using asymptotic supermomenta derived from the Weyl tensor, applicable to the case of zero cosmological constant.

Findings

New criterion for gravitational radiation based on supermomenta

Reformulation of peeling behavior with geometric construction

Energy-momentum-loss formulas including matter contributions

Abstract

This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $\Lambda$. This first paper is concerned with the case of $\Lambda =0$. Our approach is fully based on the tidal nature of the gravitational field and therefore on the `tidal energies' built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown to be fully equivalent to the classical one based on the news tensor. One of its virtues is that its formulation can be easily adapted to the case with $\Lambda>0$ covered in the second paper. We derive the general energy-momentum-loss formulae including the matter terms and all factors associated to the choices of arbitrary foliation and of super-translation. We also revisit and present a full reformulation of the traditional peeling behaviour with a neat geometrical construction that leads, in particular, to an asymptotic alignment of the supermomenta in accordance with the radiation criterion.