Time asymmetric spacetimes near null and spatial infinity. II. Expansions of developments of initial data sets with non-smooth conformal metrics

TL;DR

This paper analyzes the behavior of gravitational fields near infinity for non-conformally flat, time asymmetric initial data, revealing a hierarchy of obstructions affecting the smoothness of null infinity.

Contribution

It extends previous work by considering non-smooth conformal metrics, uncovering new obstructions to null infinity smoothness in more general initial data.

Findings

Hierarchy of obstructions to null infinity smoothness identified

Existence of spacetimes with different smoothness at future and past null infinity

Asymptotic expansions reveal data-dependent smoothness properties

Abstract

This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of initial data which are, in principle, non-conformally flat and time asymmetric. This article is the continuation of the investigation started in Class. Quantum Grav. 21 (2004) 5457-5492, where only conformally flat initial data sets were considered. For the purposes of this investigation, the conformal metric of the initial hypersurface is assumed to have a very particular type of non-smoothness at infinity in order to allow for the presence of non-Schwarzschildean initial data sets in the class under study. The calculation of asymptotic expansions of the development of these initial data sets reveals --as in the conformally flat case-- the existence of a hierarchy of obstructions to the smoothness of null infinity which are expressible in terms of the initial data. This allows for the possibility of having spacetimes where future and past null infinity have different degrees of smoothness. A conjecture regarding the general structure of the hierarchy of obstructions is presented.