Uniqueness of complete maximal hypersurfaces in spatially open (n+1)-dimensional Robertson-Walker spacetimes with flat fiber

2016/05/10 by José A. S. Pelegrín, Alfonso Romero, Rafael M. Rubio · 1 citation
Mathematics · Physics and Astronomy · #math.DG #math-ph #math.MP #msc:53C50 #msc:53C42 #msc:53C80

paper · pdf · doi:10.1007/s10714-016-2069-7

13 pages. arXiv admin note: text overlap with arXiv:1511.01422, arXiv:1401.7687

arxiv created 2016/05/10 · arxiv updated 2016/06/01

Abstract

In this paper, under natural geometric and physical assumptions we provide new uniqueness and non-existence results for complete maximal hypersurfaces in spatially open Robertson-Walker spacetimes whose fiber is flat. Moreover, our results are applied to relevant spacetimes as the steady state spacetime, Einstein-de Sitter spacetime and radiation models.

Citations

• Scalar curvature of spacelike hypersurfaces and certain class of cosmological models for accelerated expanding universes
• Constant mean curvature spacelike hypersurfaces in Lorentzian warped products and Calabi-Bernstein type problems

Cited by

• Maximal hypersurfaces in Robertson-Walker spacetimes