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Bianchi types of Lie point symmetries arising for differentially rotating stationary axisymmetric fluids
Author(s) -
Grosso R.,
Stephani H.
Publication year - 1990
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113110506
Subject(s) - homothetic transformation , killing vector field , physics , homogeneous space , perfect fluid , vector field , symmetry (geometry) , ordinary differential equation , einstein field equations , rotational symmetry , mathematical physics , classical mechanics , einstein , differential rotation , rotation (mathematics) , differential geometry , differential equation , mathematical analysis , mechanics , mathematics , geometry , quantum mechanics , magnetic field
The Einstein field equations for a perfect fluid with two commuting Killing vectors, which span the fluid's four‐velocity, are considered. A third space time symmetry, which is a homothetic or a Killing vector, can be used to reduce these equations to a system of ordinary differential equations. This symmetry restricts the form of the differential rotation Ω of the fluid. A Bianchi classification of the resulting Lie algebras is performed and related to the kinematical properties of the fluid.