U
ur Camci and Alan Barnes 2002 Class. Quantum Grav. 19 393 doi:10.1088/0264-9381/19/2/312
Ricci collineations in Friedmann–Robertson–Walker spacetimes
Uur Camci1 and Alan Barnes2
Ricci collineations and Ricci inheritance collineations of Friedmann–Robertson–Walker spacetimes are considered. When the Ricci tensor is non-degenerate, it is shown that the spacetime always admits a 15-parameter group of Ricci inheritance collineations; this is the maximal possible dimension for spacetime manifolds. The general form of the vector generating the symmetry is exhibited. It is also shown, in the generic case, that the group of Ricci collineations is six-dimensional and coincides with the isometry group. In special cases the spacetime may admit either one or four proper Ricci collineations in addition to the six isometries. These special cases are classified and the general form of the vector fields generating the Ricci collineations is exhibited. When the Ricci tensor is degenerate, the groups of Ricci inheritance collineations and Ricci collineations are infinite-dimensional. General forms for the generating vectors are obtained. Similar results are obtained for matter collineations and matter inheritance collineations.
- PACS
- MSC
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83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
- Subjects
- Dates
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Issue 2 (21 January 2002)
Received 8 October 2001, in final form 15 November 2001
Published 2 January 2002
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Ricci collineations in Friedmann–Robertson–Walker spacetimes
U
ur Camci and Alan Barnes 2002 Class. Quantum Grav. 19 393 -
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