Conformal vector fields and conformal-type collineations in space-times. (English) Zbl 0976.53073
This article discusses the existence of homothetic and conformal vector fields in spacetimes with a Killing symmetry. The study of Weyl invariants along the integral curves of the conformal vector fields leads to restrictions for the existence of such fields. A non-existence theorem for proper conformal fields in spacetimes of certain Petrov classes is given. The Bianchi I universe is discussed as an example. The relationship between conformal vector fields and Weyl collineations is studied.
Reviewer: Christian Klein (München)
MSC:
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
| 53C80 | Applications of global differential geometry to the sciences |
Keywords:
general relativity; metrics with symmetries; Killing symmetry; conformal vector field; Weyl collineationReferences:
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