Physics
Scientific paper
Feb 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005tmgm.meet.2415f&link_type=abstract
The Tenth Marcel Grossmann Meeting. Proceedings of the MG10 Meeting held at Brazilian Center for Research in Physics (CBPF), Rio
Physics
Scientific paper
The analytic study of the rotating equilibrium figures for self-gravitating fluids, has been widely explored since the time of the classical works of Newton, Maclaurin, Jacobi, Dedekind and Riemann dealing with incompressible spheroids and ellipsoids (see e.g. S. Chandrasekhar, Ellipsoidal Figures of Equilibrium 1). The structures of the equilibrium configurations of self gravitating systems was explored in a variety of theoretical approaches. Here a summary of the current state of the topic is proposed in term of: a) the classical equilibrium sequences of a homogeneous, self gravitating and rotating fluid with uniform rotation and/or vorticity, b) generalizations of the Riemann sequences (without restrictions to the shapes), c) rotating equilibrium sequences having a polytropic equation of state, d)finally, by expressing the hydrodynamic equations in a functional form, the basic conditions for the solution of the hydrodynamic equation are stated in a fully general form, permitting the study of a series of rotating self-gravitating models, depending on the velocity profiles.
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