Group classification of the characteristic initial value equations for a radiating axisymmetric, non-rotating, vacuum spacetime

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating spacetime 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...

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Veröffentlicht in:Classical and quantum gravity 2007-12, Vol.24 (23), p.6007-6017
Hauptverfasser: Ibragimov, Nail H, Wessels, Ewald J H, Ellis, George F R
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Sprache:eng
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Zusammenfassung:We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating spacetime 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 spacetime. We find that the equations admit a five-dimensional equivalence Lie algebra. The initial value function that allows the equations to admit a non-trivial Lie symmetry separates into three disjoint equivalence classes.
ISSN:0264-9381
1361-6382
1361-6382
DOI:10.1088/0264-9381/24/23/020