Mass and stability of rigidly rotating relativistic polytropes by energy method

The energy of a rigidly rotating star is written in the first and second post-Newtonian approximation. Conditions for equilibrium and stability are derived, as well as evolutionary paths for stars shedding angular momentum or mass. For polytropic index n>1, these analytic results agree with exact numerical results to within a few percent as long the general relativity index (P/rhoc2)/subc/<0.1. The energy method is applied to low mass white dwarfs, to semirelativistic neutron stars and to supermassive stars