Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985mnras.212...23c&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 212, Jan. 1, 1985, p. 23-55.
Astronomy and Astrophysics
Astronomy
67
Black Holes (Astronomy), Celestial Mechanics, Compressibility Effects, Stellar Evolution, Stellar Models, Stellar Motions, Angular Momentum, Equations Of Motion, Equilibrium Equations, Hydrodynamic Equations, Stellar Structure, Tides
Scientific paper
A study is undertaken of the intrinsic mechanical properties of a wide class of simplified affine star models, characterized in terms of a 3 x 3 deformation matrix, independently of any particular physical context. The canonical equations of internal motion are noted to be the same as those obtainable through an application of the tensor virial theorem to the first terms in a Taylor expansion about the center of a corresponding Newtonian hydrodynamic model. An extension to the general compressible case of the classical Dedekind theorem for incompressible fluid models arises from the discrete symmetry of the Lagrangian L(I) under the operation of replacing the deformation matrix by its transpose. After a discussion of the mechanical properties arising from these symmetries, it is shown that any equilibrium state of a general, compressible affine star model is conformally related to one of the equilibrium states of the corresponding incompressible fluid model.
Carter Brandon
Luminet Jean-Pierre
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