Complete classification of Noether conservation laws for a physically significant stationary Kaluza-Klein perfect fluid solution

Document Type : Original Article

Author

Fatemeh Ahangari

Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

10.22034/kjm.2024.417760.3007

Abstract

Steady rigid rotation of a fluid in general relativity has been remarkably tackled by many authors specifically after Godel proposed relativistic model of a rotating dust universe. Considering the fact that stationary Kaluza-Klein perfect fluid models in standard Einstein theory are not available in literature, the significance of obtaining and analyzing such solutions in order to investigate the effects of dimensionality on the different physical parameters is undoubtedly undeniable. In this paper, the problem of symmetries and conservation laws for some specific solutions of Kaluza-Klein field equations for stationary symmetric fluid models in standard Einstein theory is exhaustively analyzed. For this purpose, a physically viable stationary Kaluza-Klein perfect fluid solution is considered and the corresponding point generators of one parameter Lie groups of transformations that leave invariant the action integral associated to the Lagrangian, namely, Noether symmetries are computed and a brief discussion regarding the structure of the Lie algebra of Noether symmetries from the algebraic point of view is presented. Moreover, a complete classification of the resulted Noether symmetry subalgebras is proposed by constructing an optimal system of one-dimensional subalgebras via the adjoint representation. Besides the Killing vector fields of our analyzed geodesic Lagrangian are totally determined. Significantly, all the corresponding conservation laws of the Euler-Lagrange (geodesic) equations concluded from the obtained Noether symmetries are comprehensively calculated.

Keywords

Kaluza-Klein model

rotating fluids

Noether symmetries

Killing vector fields

conservation laws

Subjects

• 53 Differential geometry

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