Null hypersurfaces in generalized Robertson–Walker spacetimes
| Autor: | Didier A. Solis, Oscar Palmas, Matias Navarro |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Quadric Mathematics::Complex Variables 010102 general mathematics Null (mathematics) Mathematical analysis General Physics and Astronomy Space form Space (mathematics) 01 natural sciences Ambient space General Relativity and Quantum Cosmology Mathematics::Algebraic Geometry Hyperplane De Sitter universe 0103 physical sciences Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology Anti-de Sitter space 0101 mathematics Mathematical Physics Mathematics |
| Zdroj: | Journal of Geometry and Physics. 106:256-267 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2016.04.009 |
| Popis: | We study the geometry of null hypersurfaces M in generalized Robertson–Walker spacetimes. First we characterize such null hypersurfaces as graphs of generalized eikonal functions over the fiber and use this characterization to show that such hypersurfaces are parallel if and only if their fibers are also parallel. We further use this technique to construct several examples of null hypersurfaces in both de Sitter and anti de Sitter spaces. Then we characterize all the totally umbilical null hypersurfaces M in a Lorentzian space form (viewed as a quadric in a semi-Euclidean ambient space) as intersections of the space form with a hyperplane. Finally we study the totally umbilical spacelike hypersurfaces of null hypersurfaces in space forms and characterize them as planar sections of M . |
| Databáze: | OpenAIRE |
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