A simple characterization of generalized Robertson–Walker spacetimes
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A generalized Robertson–Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of generalized Robertson–Walker spacetimes widely extends the one of classical Robertson–Walker spacetimes. Further, generalized Robertson–Walker spacetimes appear as a privileged class of inhomogeneous spacetimes admitting an isotropic radiation.
In this section we prove a very simple characterization of generalized Robertson–Walker spacetimes; namely, a Lorentzian manifold is a generalized Robertson–Walker spacetime if and only if it admits a timelike concircular vector field.
KeywordsGeneralized Robertson–Walker spacetime Robertson–Walker spacetime Timelike concircular vector field Lorentzian warped product
Mathematics Subject ClassificationPrimary 83F05 Secondary 53C25
The author thanks the referees for their useful suggestions for improving the presentation of this paper.
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