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On the definition of cylindrical symmetry. (English) Zbl 0935.83002

Summary: The standard definition of cylindrical symmetry in general relativity is reviewed. Taking the view that axial symmetry is an essential prerequisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of the isometry group should be dropped, which leads to a new, more general definition of cylindrical symmetry. Stationarity and staticity in cylindrically symmetric spacetimes are then defined, and these issues are analysed in connection with orthogonal transitivity, thus proving some new results on the structure of the isometry group for this class of spacetimes.

MSC:

83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
83F05 Relativistic cosmology
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