Curvature conditions for spatial isotropy

doi:10.1016/j.geomphys.2022.104557

CSpace

	Curvature conditions for spatial isotropy
	Tzanavaris, Kostas 1; Seoane, Pau Amaro 2,3,4,5
	2022-08-01
发表期刊	JOURNAL OF GEOMETRY AND PHYSICS
ISSN	0393-0440
卷号	178 页码:14
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.
关键词	General relativity Differential geometry Riemannian geometry
DOI	10.1016/j.geomphys.2022.104557
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics ; Physics, Mathematical
WOS记录号	WOS:000806873000003
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61245
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.