The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations
type: Item
instance of: scholarly article
title: The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations
zbMATH Open document ID: 0613.53048
DOI: 10.1007/BF01208959
author: Demetrios Christodoulou
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The paper is the continuation of author's previous papers [ibid. 105, 337-362 (1986; Zbl 0608.35039), and 106, 587-622 (1986; see the preceding review)] on the global existence of generalized solutions of spherically symmetric Einstein-scalar field equations \(R_{\mu \nu}=8\pi \partial_{\mu}\phi \partial_{\nu}\phi\), in the large. In terms of a retarded time coordinate u and a radial coordinate r, the metric is taken to be of the form \[ ds^ 2=-e^{2\nu} du^ 2-2e^{\nu +\lambda} du dr+r^ 2 d\Sigma^ 2, \] where \(d\Sigma^ 2\) is the metric of the standard 2-sphere. In this paper, the regularity properties of the space- time and the scalar field corresponding to a generalized solution, including the behavior of the generalized solution at null infinity, are studied. The uniqueness theorem is stated and proved in the following form: ''A generalized solution'' having the same data as a classical solution coincides with it in the domain of existence of the latter.''
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 83C20
Mathematics Subject Classification ID: 83C40
zbMATH DE Number: 3992384
zbMATH Keywords: global initial value problem
zbMATH Keywords: generalized solutions
zbMATH Keywords: Einstein-scalar field equations
zbMATH Keywords: uniqueness theorem
MaRDI profile type: Publication
cites work: The problem of a self-gravitating scalar field
cites work: Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large
cites work: Partial regularity of suitable weak solutions of the navier-stokes equations
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description: scientific article; zbMATH DE number 3992384