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Some remarks on locally conformally flat static space-times. (English) Zbl 1076.53084

Summary: Necessary and sufficient conditions for a static space–time to be locally conformally flat are obtained, showing some significant restrictions on the possible warping functions of the space–times. This occurs in opposition to cosmological models, where Robertson–Walker space–times are locally conformally flat for any warping function.

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
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