A global analysis approach to the general relativistic fluid ball problem
type: Item
instance of: scholarly article
title: A global analysis approach to the general relativistic fluid ball problem
zbMATH Open document ID: 0546.53048
DOI: 10.1007/BF00756470
author: H. P. Künzle
author: J. R. Savage
published in: General Relativity and Gravitation
publication date: 1980-01-01T00:00:00Z
review text: This paper studies the conjecture that the Einstein equations require that every bounded, static, perfect fluid solution in otherwise empty, asymptotically flat space, is necessarily spherically symmetric. Physical intuition strongly supports this conjecture, which is easily shown to be true for Newtonian gravity. A weakened form of this conjecture is established in this paper: If a family of static perfect fluid solutions of fixed total mass depends differentiably on one parameter and contains the spherically symmetric one, then every member of the family is diffeomorphic (and thus physically equivalent) to it. The global methods of \textit{A. E. Fischer} and \textit{J. E. Marsden} are used [Differ. Geom., Proc. Symp. Pure Math. 27, Part 2, 219-263 (1975; Zbl 0314.53031) and Duke Math. J. 42, 519-547 (1975; Zbl 0336.53032)].
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 58D17
Mathematics Subject Classification ID: 83C15
Mathematics Subject Classification ID: 83C20
Mathematics Subject Classification ID: 83C55
zbMATH DE Number: 3870164
zbMATH Keywords: Einstein equations
zbMATH Keywords: perfect fluid solution
zbMATH Keywords: asymptotically flat space
reviewed by: Carl H. Brans
MaRDI profile type: Publication
cites work: Q5338091
cites work: Some decompositions of the space of symmetric tensors on a Riemannian manifolds
cites work: Q3882984
cites work: Perfect fluid flows over \(\mathbb{R}^n\) with asymptotic conditions
cites work: Q4187039
cites work: Q4194080
cites work: Q4163831
cites work: Q5605734
cites work: Deformations of the scalar curvature
cites work: The Manifold of Conformally Equivalent Metrics
cites work: The Large Scale Structure of Space-Time
cites work: Equilibrium of slowly rotating relativistic fluids
cites work: Q5649693
cites work: Q5849608
cites work: The null spaces of elliptic partial differential operators in R\(^n\)
cites work: A simple proof of the generalization of Israel's theorem
description: scientific article; zbMATH DE number 3870164