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

Ibragimov, Nail H.; Wessels, Ewald J. H.; Ellis, George F. R.

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

Authors

Ibragimov, Nail H.

Wessels, Ewald J. H.

Ellis, George F. R.

Description

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.
18 Pages. Submitted to Classical and Quantum Gravity