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 spac...

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Bibliographic Details
Published in:arXiv.org 2006-11
Main Authors: Ibragimov, Nail H, Wessels, Ewald J H, Ellis, George F R
Format: Article
Language:English
Subjects:
Lie groups
Mathematical analysis
Rotation
Spacetime
Tensors
Time dependence
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0611109