Does asymptotic simplicity allow for radiation near spatial infinity?

TL;DR

This paper investigates whether asymptotic simplicity in general relativity allows for smooth gravitational radiation near spatial infinity, revealing that non-static initial data typically lead to singularities at null infinity.

Contribution

It demonstrates that generic time symmetric initial data with analytic conformal metrics produce logarithmic singularities at null infinity, and proposes that only static data yield smooth null infinity.

Findings

Logarithmic singularities arise from non-static initial data.

Static initial data lead to non-singular, smooth null infinity.

Conjecture: only static data produce developments with smooth null infinity.

Abstract

A representation of spatial infinity based in the properties of conformal geodesics is used to obtain asymptotic expansions of the gravitational field near the region where null infinity touches spatial infinity. These expansions show that generic time symmetric initial data with an analytic conformal metric at spatial infinity will give rise to developments with a certain type of logarithmic singularities at the points where null infinity and spatial infinity meet. These logarithmic singularities produce a non-smooth null infinity. The sources of the logarithmic singularities are traced back down to the initial data. It is shown that is the parts of the initial data responsible for the non-regular behaviour of the solutions are not present, then the initial data is static to a certain order. On the basis of these results it is conjectured that the only time symmetric data sets with developments having a smooth null infinity are those which are static in a neighbourhood of infinity. This conjecture generalises a previous conjecture regarding time symmetric, conformally flat data. The relation of these conjectures to Penrose's proposal for the description of the asymptotic gravitational field of isolated bodies is discussed.