Axial symmetry and conformal Killing vectors

Details Axial symmetry and conformal Killing vectors Axial symmetry and conformal Killing vectors

2002-01-14

arxiv.org/abs/gr-qc/0201045v1

Class.Quant.Grav.10:1633-1647,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, Latex, no figures

Scientific paper

10.1088/0264-9381/10/8/020

Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, we prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others mush vanish or else the symmetry is larger than that originally considered. The results are completely general and do not depend on Einstein's equations or any particular matter content.

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