Complete spacelike hypersurfaces in generalized Robertson–Walker and the null convergence condition: Calabi–Bernstein problems

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• 作者：Juan A. Aledo ; Rafael M. Rubio…
• 关键词：Spacelike hypersurface ; Constant mean curvature ; Generalized Robertson Walker spacetime ; Null convergence condition ; Spatially parabolic spacetime ; Calabi–Bernstein problem
• 刊名：Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：1
• 页码：115-128
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Milan
• ISSN：1579-1505
• 卷排序：111

文摘

We study constant mean curvature spacelike hypersurfaces in generalized Robertson–Walker spacetimes \(\overline{M}= I \times _f F\) which are spatially parabolic (i.e. its fiber F is a (non-compact) complete Riemannian parabolic manifold) and satisfy the null convergence condition. In particular, we provide several rigidity results under appropriate mathematical and physical assumptions. We pay special attention to the case where the GRW spacetime is Einstein. As an application, some Calabi–Bernstein type results are given.