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On Geometric Analysis of the Dynamics of Volumetric Expansion and its Applications to General Relativity

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Abstract

In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its applications to the problem of the existence in the space-time of compact and complete spacelike hypersurfaces and to the global geometry of generalized Robertson–Walker space-times.

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Author information

Correspondence to S. E. Stepanov.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 146, Geometry, 2018.

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Stepanov, S.E., Denezhkina, I.E. & Ovchinnikov, A.V. On Geometric Analysis of the Dynamics of Volumetric Expansion and its Applications to General Relativity. J Math Sci 245, 659–668 (2020). https://doi.org/10.1007/s10958-020-04715-2

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Keywords and phrases

  • volumetric expansion
  • vector field
  • flow
  • space-time
  • spacelike hypersurface

AMS Subject Classification

  • 53C25
  • 53Z05