Group classification of the Sachs equations for a radiating   axisymmetric, non-rotating, vacuum space-time
  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. 
Nail H. Ibragimov (1), Ewald J. H. Wessels (2) and George F. R. Ellis   (2) ((1) Research Centre ALGA: Advances in Lie Group...