Nonexistence of Multiple Black Holes in Stationary Analytic Vacuum spacetimes

We prove the nonexistence of non-rotating and degenerate horizon components in the stationary, asymptotically flat, $I^+$-regular, analytic vacuum spacetime. This result rules out the final case in the classification of stationary analytic black-hole spacetimes. Consequently, the stationary, asymptotically flat, $I^+$-regular, analytic vacuum black hole uniqueness conjecture is settled affirmatively in full.