Invariant form of spin-transfer switching condition

We derive an invariant form of the current-induced switching condition in spin-transfer devices and show that for energy minima and maxima the "switching ability" of the current is determined by the spin torque divergence. In contrast, energy saddle points are normally stabilized by current-induced merging with other equilibria. Our approach provides new predictions for several experimental setups and shows the limitations of some frequently used approximations.