On the definition of cylindrical symmetry

Details On the definition of cylindrical symmetry On the definition of cylindrical symmetry

1999-05-18

arxiv.org/abs/gr-qc/9905059v1

Class.Quant.Grav. 16 (1999) 3025-3034

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX, no figures

Scientific paper

10.1088/0264-9381/16/9/318

The standard definition of cylindrical symmetry in General Relativity is reviewed. Taking the view that axial symmetry is an essential pre-requisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of the isometry group should be dropped, this leading 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.

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