Curvature conditions for spatial isotropy
文献类型：期刊论文
| 作者 | Tzanavaris, Kostas1; Seoane, Pau Amaro2,3,4,5 |
| 刊名 | JOURNAL OF GEOMETRY AND PHYSICS
 |
| 出版日期 | 2022-08-01 |
| 卷号 | 178页码:14 |
| 关键词 | General relativity Differential geometry Riemannian geometry |
| ISSN号 | 0393-0440 |
| DOI | 10.1016/j.geomphys.2022.104557 |
| 英文摘要 | In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalized) Robertson-Walker space-time is important. In particular, it is a requirement for the development of initial data to reproduce or approximate the standard cosmological model. Usually these conditions involve the Einstein field equations, which change if one considers alternative theories of gravity or if the coupling matter fields change. Therefore, the derivation of conditions which do not depend on the field equations is an advantage. In this work we present a geometric derivation of such a condition. We require the existence of a unit vector field to distinguish at each point of space two (non-equal) sectional curvatures. This is equivalent for the Riemann tensor to adopt a specific form. Our geometrical approach yields a local isometry between the space and a Robertson-Walker space of the same dimension, curvature and metric tensor sign (the dimension of the largest subspace on which the metric tensor is negative definite). Remarkably, if the space is simply-connected, the isometry is global. Our result generalizes to a class of spaces of non-constant curvature the theorem that spaces of the same constant curvature, dimension and metric tensor sign must be locally isometric. Because we do not make any assumptions regarding field equations, matter fields or metric tensor sign, one can readily use this result to study cosmological models within alternative theories of gravity or with different matter fields. (C) 2022 Elsevier B.V. All rights reserved. |
| 资助项目 | National Key R&D Program of China[2016YFA0400702] ; National Science Foun-dation of China[11721303] ; National Science Foun-dation of China[11873022] ; National Science Foun-dation of China[11991053] |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000806873000003 |
| 出版者 | ELSEVIER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/61244]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Seoane, Pau Amaro |
| 作者单位 | 1.Univ Edinburgh, Higgs Ctr Theoret Phys, Sch Phys & Astron, Edinburgh, Scotland 2.Univ Politecn Valencia, Inst Multidisciplinary Math, Valencia, Spain 3.Max Planck Inst Extraterr Phys, Munich, Germany 4.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing, Peoples R China 5.Kavli Inst Astron & Astrophys, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Tzanavaris, Kostas,Seoane, Pau Amaro. Curvature conditions for spatial isotropy[J]. JOURNAL OF GEOMETRY AND PHYSICS,2022,178:14. |
| APA | Tzanavaris, Kostas,&Seoane, Pau Amaro.(2022).Curvature conditions for spatial isotropy.JOURNAL OF GEOMETRY AND PHYSICS,178,14. |
| MLA | Tzanavaris, Kostas,et al."Curvature conditions for spatial isotropy".JOURNAL OF GEOMETRY AND PHYSICS 178(2022):14. |
入库方式： OAI收割
来源：数学与系统科学研究院
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