Spatial metrics which are static in many ways
type: Item
instance of: scholarly article
title: Spatial metrics which are static in many ways
zbMATH Open document ID: 0981.83014
DOI: 10.1023/A:1001986116619
published in: General Relativity and Gravitation
publication date: 2001-02-11T00:00:00Z
review text: Given a spatial (i.e. 3-dimensional and positive definite) metric \(h_{ab}(x^1,x^2,x^3) dx^a dx^b\), one may look for a real-valued function \(N(x^1,x^2,x^3)\) such that the 4-dimensional static Lorentzian metric \(-N(x^1,x^2,x^3)^2 dt^2+ h_{ab}(x^1,x^2,x^3) dx^a dx^b\) satisfies Einstein's vacuum field equation, possibly with a cosmological constant. In this paper the author determines all cases in which this problem has two different solutions \(N=N_1\) and \(N=N_2\). The resulting Lorentzian metrics turn out to be all of Petrov type \(D\). The locally rotationally symmetric Kasner metric is an example.
reviewed by: Volker Perlick
Mathematics Subject Classification ID: 83C20
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1562777
zbMATH Keywords: Einstein's vacuum field equation
zbMATH Keywords: Petrov type \(D\)
zbMATH Keywords: locally rotationally symmetric Kasner metric
author: K. P. Tod
MaRDI profile type: Publication
cites work: Q3896182
cites work: Quasi-Newtonian dust cosmologies
cites work: Newtonian-like congruences
cites work: On a Special Class of Type-I Gravitational Fields
cites work: On shear free normal flows of a perfect fluid
full work available at URL: a:1001986116619
OpenAlex ID: W1537757396
description: scientific article; zbMATH DE number 1562777