General relativity in a \((2+1)\)-dimensional space-time: An electrically charged solution
type: Item
instance of: scholarly article
title: General relativity in a \((2+1)\)-dimensional space-time: An electrically charged solution
zbMATH Open document ID: 0604.53037
DOI: 10.1007/BF01090483
author: J. Richard III Gott
author: Jonathan Z. Simon
author: Mark Alpert
published in: General Relativity and Gravitation
publication date: 1986-01-01T00:00:00Z
review text: The authors solve the Einstein-Maxwell equation in \(2+1\) dimensions, in the case that the only nonvanishing components of the electromagnetic field are \(F^{01}=-F^{10}=E(r)\) (stationary and radially-symmetric case). They obtain \(E(r)=Q/r\) and the metric \[ ds^ 2=-A(r)dt^ 2+[A(r)]^{-1}dr^ 2+r^ 2d\Phi^ 2, \] where \(A(r)=(kQ^ 2/2\pi)\ln (r_ c/r)\), Q is the electrical charge and \(r_ c\) an integration constant, independent of Q. The singularities will be at \(r=0\), \(r=r_ c\) and \(r\to \infty\). The case \(r=r_ m\), in which \(A(r_ m)=1\), is of a particular interest. The authors also study the Kruskal extension of this solution and arrive at some conclusions comparing the above solution with the Kaluza-Klein formalism.
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 83C15
zbMATH DE Number: 3975814
zbMATH Keywords: Einstein-Maxwell equation
zbMATH Keywords: electromagnetic field
zbMATH Keywords: Kruskal extension
zbMATH Keywords: Kaluza-Klein formalism
reviewed by: I. Gottlieb
MaRDI profile type: Publication
cites work: Einstein's theory in a three-dimensional space-time
cites work: Q5670643
description: scientific article; zbMATH DE number 3975814