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

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

2006-11-21

arxiv.org/abs/gr-qc/0611109v1

Class.Quant.Grav.24:6007-6017,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 Pages. Submitted to Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/24/23/020

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.

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