Stationary axisymmetric perfect fluid solutions in general relativity
type: Item
instance of: scholarly article
title: Stationary axisymmetric perfect fluid solutions in general relativity
zbMATH Open document ID: 0642.53080
DOI: 10.1007/BF00758968
author: Eduard Herlt
published in: General Relativity and Gravitation
publication date: 1988-01-01T00:00:00Z
review text: A new class of exact solutions of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. The class of solutions is invariantly characterized by means of the following properties: (i) The energy-momentum tensor describes a perfect fluid. (ii) There are two commuting Killing vectors \(\xi\) and \(\eta\) which form an abelian group \(G_ 2\) of motion. (iii) There is a timelike Killing vector parallel to the four-velocity of the fluid (rigid rotation of the fluid). (iv) The four-vector of the angular velocity of the fluid is a gradient \(\Omega^ i=-(1/4c)\epsilon^{irkl}U_ l(U_{r;k}- U_{k;r})=\chi^{'i}.\) The last assumption is the reason that all solutions of this class can be found by solving an ordinary differential equation of the second order.
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 83C20
zbMATH DE Number: 4046618
zbMATH Keywords: exact solutions
zbMATH Keywords: Einstein's field equations
zbMATH Keywords: perfect fluid
zbMATH Keywords: Killing vectors
zbMATH Keywords: angular velocity
MaRDI profile type: Publication
cites work: Rigidly rotationg perfect fluids
description: scientific article; zbMATH DE number 4046618