Asymptotically Shear-free and Twist-free Null Geodesic Congruences

TL;DR

This paper identifies rare asymptotically flat space-times with null geodesic congruences that are both shear-free and twist-free, including Robinson-Trautman space-times, and discusses their unique properties.

Contribution

It characterizes the class of space-times with these special congruences and shows how to find them, highlighting their uniqueness within the broader context.

Findings

Existence of rare asymptotically flat space-times with shear-free, twist-free null congruences

Robinson-Trautman space-times are a special case of this class

Such congruences are isolated with no neighboring congruences sharing these properties

Abstract

We show that, though they are rare, there are asymptotically flat space-times that possess null geodesic congruences that are both asymptotically shear- free and twist-free (surface forming). In particular, we display the class of space-times that possess this property and demonstrate how these congruences can be found. A special case within this class are the Robinson- Trautman space-times. In addition, we show that in each case the congruence is isolated in the sense that there are no other neighboring congruences with this dual property.