On the symmetries of equilibrium stellar models

The equilibrium states of isolated self-gravitating fluids (i.e. stellar models) always have a high degree of spatial symmetry. This paper reviews the current understanding of these symmetries in both the newtonian and the general relativistic theories. The arguments that establish (under various appropriate conditions) the necessity of spherical symmetry, axisymmetry, and reflection symmetry are summarized. The limitations of the present results and suggestions for further progress are outlined in the concluding remarks.