On Mason's rigidity theorem

TL;DR

This paper proves a rigidity theorem for certain vacuum space-times, showing that under specific smoothness and transversality conditions, such space-times cannot be algebraically special, with implications for the structure of gravitational fields.

Contribution

It introduces a new rigidity theorem for the Trautman-Bondi mass and extends Mason's argument to exclude certain algebraically special space-times under smoothness assumptions.

Findings

No algebraically special asymptotically simple vacuum space-times with smooth shear-free congruences exist under the given conditions.

A new rigidity theorem for the Trautman-Bondi mass is established.

The proof relies on extending Mason's argument and analyzing the properties of null congruences.

Abstract

Following an argument proposed by Mason, we prove that there are no algebraically special asymptotically simple vacuum space-times with a smooth, shear-free, geodesic congruence of principal null directions extending transversally to a cross-section of Scri. Our analysis leaves the door open for escaping this conclusion if the congruence is not smooth, or not transverse to Scri. One of the elements of the proof is a new rigidity theorem for the Trautman-Bondi mass.