Perfect fluids from high power sigma-models
type: Item
instance of: scholarly article
zbMATH Open document ID: 1244.53025
DOI: 10.1142/S0219887811005919
published in: International Journal of Geometric Methods in Modern Physics
publication date: 2012-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1006.1133
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 49Q99
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 6046009
zbMATH Keywords: perfect fluid
zbMATH Keywords: relativistic fluid
zbMATH Keywords: variational method
zbMATH Keywords: harmonic submersion
zbMATH Keywords: Lorentz manifold
author: Radu Slobodeanu
MaRDI profile type: Publication
arXiv ID: 1006.1133
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title: Perfect fluids from high power sigma-models
review text: A perfect fluid on a space-time \((M,g)\) is a triple \((U,\rho,p)\) such that: (i) \(U\) is a time-like future-pointing unit vector field on \(M\), called the flow vector field, (ii) \(\rho, p:M\to\mathbb R\) are the mass (energy) density and pressure, respectively, (iii) \(\text{div}\,T=0\), where \(T\) is the stress-energy tensor given by \(T=p\,g+(p+\rho)\,\omega\otimes\omega\), with the \(1\)-form \(\omega=U^\flat\) metrically equivalent to \(U\).NEWLINENEWLINEThe fact that perfect fluid dynamics admits a Lagrangian formulation is widely known. The Lagrangian is given in terms of a dual variable \(\varphi\) that is a submersion defined on the space-time such that the fluid velocity four-vector spans its vertical foliation. It is interesting to notice that the sextic Lagrangian is exactly the extension of the Skyrme model. In fact, the equations for all perfect fluids with cosmological equation of state are generated in a similar way by raising to a proper power this sextic Lagrangian.NEWLINENEWLINEIn this paper, the author presents these constructions in the standard differential geometric setup. The following topics are addressed: the geometric interpretation of the Euler equations for the fluid equations for the field, the effect of conformal change of metrics, the irrational case, the sheer-free case in relation with the harmonic morphisms theory, and the coupling with gravity.
reviewed by: Andrew Bucki
description: scientific article; zbMATH DE number 6046009