Group classification of the Sachs equations for a radiating axisymmetric, non-rotating, vacuum space-time

TL;DR

This paper performs a Lie group analysis of Sachs equations in a specific vacuum spacetime, identifying symmetries that define a special class of geometrically significant solutions.

Contribution

It identifies conditions under which Sachs equations admit Lie symmetries, revealing a new class of geometrically special vacuum spacetimes.

Findings

A particular initial data form admits Lie symmetry.

Defines a special class of axisymmetric, non-rotating vacuum spacetimes.

Highlights physical relevance of the symmetric solutions.

Abstract

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.