A family of cylindrically symmetric solutions to Einstein-Maxwell equations
type: Item
instance of: scholarly article
title: A family of cylindrically symmetric solutions to Einstein-Maxwell equations
zbMATH Open document ID: 0831.53062
DOI: 10.1007/BF02108069
author: Canbin Liang
published in: General Relativity and Gravitation
publication date: 1996-02-12T00:00:00Z
review text: Observing that the scalar curvature vanishes due to the tracelessness of the energy-momentum tensor of the em (electromagnetic) field and writing the NP (Newman-Penrose) equations in this case, the author quotes the form of source-free Maxwell equations [\textit{D. Kramer, H. Stephani, E. Herlt and M. MacCallum}, Exact solutions of Einstein's field equations (Cambridge 1980; Zbl 0449.53018)] in terms of the tetrad components \(\Phi_0\), \(\Phi_1\) and \(\Phi_2\) of the em 2-form \(F\). Consequently, it is stressed that in the case \(\Phi_0 = \Phi_2\), implied by the last two NP equations, the em field admits one more symmetry than the cylindrically symmetric metric, in which case the former quantity is referred to as plane symmetric (otherwise semi-plane symmetric). In the case \(\Phi_1 = 0\) the electromagnetic field and the metric admit the same symmetries. Focusing on the case \(\Phi_1 = 0\) \((\Phi_1 \neq 0, \Phi_2 \neq 0)\), the author derives a family of cylindrically symmetric solutions to the Einstein-Maxwell equations. The metric associated with these solutions is written in terms of some undetermined functions, and the non-vanishing components of the em field \(F\) are derived. Finally it is demonstrated that the Petrov type of the Weyl tensor of the metric is of type II.
reviewed by: Serban Misicu
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83C60
Mathematics Subject Classification ID: 83C22
Mathematics Subject Classification ID: 83C20
zbMATH DE Number: 792895
zbMATH Keywords: Newton-Penrose equations
zbMATH Keywords: Killing vector fields
zbMATH Keywords: cylindrically symmetric metric
zbMATH Keywords: Einstein-Maxwell equations
zbMATH Keywords: Weyl tensor
MaRDI profile type: Publication
cites work: Q3896182
cites work: Static ‘‘semi-plane-symmetric’’ metrics yielded by plane-symmetric electromagnetic fields
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description: scientific article; zbMATH DE number 792895