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On uniqueness of the foliation by comoving observers restspaces of a Generalized Robertson–Walker spacetime

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Abstract

A characterization of the foliation by spacelike slices of an \((n+1)\)-dimensional spatially closed Generalized Robertson–Walker spacetime is given by means of studying a natural mean curvature type equation on spacelike graphs. Under some natural assumptions, of physical or geometric nature, all the entire solutions of such an equation are obtained. In particular, the case of entire spacelike graphs in de Sitter spacetime is faced and completely solved by means of a new application of a known integral formula.

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Acknowledgements

The authors would like to thank the referee for his deep reading and useful suggestions to improve this article, especially those concerning Remark 6 and Theorem 7. The authors are partially supported by Spanish MINECO and ERDF Project MTM2013-47828-C2-1-P.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    José A. S. Pelegrín & Alfonso Romero

  2. Departamento de Matemáticas, Campus de Rabanales, Universidad de Córdoba, 14071, Córdoba, Spain

    Rafael M. Rubio

Authors
  1. José A. S. Pelegrín
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  2. Alfonso Romero
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  3. Rafael M. Rubio
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Correspondence to José A. S. Pelegrín.

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Pelegrín, J.A.S., Romero, A. & Rubio, R.M. On uniqueness of the foliation by comoving observers restspaces of a Generalized Robertson–Walker spacetime. Gen Relativ Gravit 49, 16 (2017). https://doi.org/10.1007/s10714-016-2183-6

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  • DOI: https://doi.org/10.1007/s10714-016-2183-6

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