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A simple characterization of generalized Robertson–Walker spacetimes

  • Bang-Yen ChenEmail author
Research Article

Abstract

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.

Keywords

Generalized Robertson–Walker spacetime Robertson–Walker spacetime Timelike concircular vector field  Lorentzian warped product 

Mathematics Subject Classification

Primary 83F05 Secondary 53C25 

Notes

Acknowledgments

The author thanks the referees for their useful suggestions for improving the presentation of this paper.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

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