Asymptotic Structure with a positive cosmological constant

TL;DR

This paper develops a covariant, gauge-invariant framework to analyze gravitational radiation at infinity in space-times with positive cosmological constant, using Weyl curvature and the Bel-Robinson tensor.

Contribution

It introduces a new asymptotic structure based on triplet data and proposes criteria for gravitational radiation and no-incoming radiation in $ ext{dS}$-like space-times.

Findings

Defines a triplet $( ext{scri},h_{ab},D_{ab})$ encoding asymptotic properties.

Proposes a no-incoming radiation criterion based on the triplet and supermomenta.

Identifies components of news tensors associated with cross-sections of $ ext{scri}$.

Abstract

This is the second of two papers that study the asymptotic structure of space-times with a non-negative cosmological constant $\Lambda$. This paper deals with the case $\Lambda >0$. Our approach is founded on the `tidal energies' built with the Weyl curvature and, specifically, we use the asymptotic super-Poynting vector computed from the rescaled Bel-Robinson tensor at infinity to provide a covariant, gauge-invariant, criterion for the existence, or absence, of gravitational radiation at infinity. The fundamental idea we put forward is that the physical asymptotic properties are encoded in $(\scri,h_{ab},D_{ab})$, where the first element of the triplet is a 3-dimensional manifold, the second is a representative of a conformal class of Riemannian metrics on $\scri$, and the third element is a traceless symmetric tensor field on $\scri$. We similarly propose a no-incoming radiation criterion based also on the triplet $(\scri,h_{ab},D_{ab})$ and on radiant supermomenta deduced from the rescaled Bel-Robinson tensor too. We search for news tensors and argue that any news-like object must be associated to, and depends on, 2-dimensional cross-sections of $\scri$. We identify one component of news for every such cross-section and present a general strategy to find the second component. We also introduce the concept of equipped $\scri$, consider the limit $\Lambda\rightarrow 0$ and apply all our results to selected exact solutions of Einstein Field Equations. The full-length abstract is available in the paper.