Marek Szydłowski and Andrzej J Maciejewski 2004 J. Phys. A: Math. Gen. 37 3501 doi:10.1088/0305-4470/37/10/013
Marek Szydłowski1 and Andrzej J Maciejewski2
Show affiliationsIt is proposed to use the Lie group theory of symmetries of differential equations to investigate the system of equations describing a static star in a radiative and convective equilibrium. It is shown that the action of an admissible group induces a certain algebraic structure in the set of all solutions, which can be used to find a family of new solutions. We have demonstrated that, in the most general case, the equations admit an infinite parameter group of quasi-homologous transformations. We have found invariants of the symmetry groups which correspond to the fundamental relations describing a physical characteristic of the stars such as the Hertzsprung–Russell diagram or the mass–luminosity relation. In this way we can suggest that group invariants have not only purely mathematical sense, but their forms are closely associated with the basic empirical relations.
97.10.Cv Stellar structure, interiors, evolution, nucleosynthesis, ages
85A15 Galactic and stellar structure
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
Issue 10 (12 March 2004)
Received 25 August 2003, in final form 22 January 2004
Published 24 February 2004
Marek Szydłowski and Andrzej J Maciejewski 2004 J. Phys. A: Math. Gen. 37 3501
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