Slowly Rotating Relativistic Stars. III. Static Criterion for Stability

A method is given for analyzing the stabilizing effect of a slow and rigid rotation on the radial pu~sa- tions of relativistic stellar models. This method is restricted to stellar models with a one-parameter equa- tion of state, (P = ~P(~), for which the adiabatic index is F = (~ + cP)~P'(dcP/d8)-e.g., white dwarfs and neutron stars. The method is also applicable to hot, isentropic stellar mode's. The method does not involve solving the full dynamical equations for the pulsations of the rotating star; instead, it involves constructing a family of equilibrium configurations with a specified nonrigid rotation, and then comparing the masses or binding energies of these configurations with the masses or binding energies of the uni- formly rotating models. Hence, this method is the generalization to slowly rotating stars of the "static stability analysis," which is now used widely for nonrotating stellar model

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