Kerr Black Hole Uniqueness

Abstract: We prove the black hole uniqueness conjecture in the axially symmetric, stationary, vacuum setting: there is no regular asymptotically flat configuration with more than one horizon component when every degenerate component has nonzero angular momentum. More precisely, it is shown that in any such multi-horizon configuration, the logarithmic angle defect along every finite axis rod is strictly negative, and hence the interaction force along such axis rods is always attractive. The proof is based on a refined asymptotic analysis of the associated singular harmonic maps, in part from the companion paper [16], together with a global bound for the Weyl conformal factor arising from a certain scalar curvature related differential inequality. Furthermore, as a corollary of the extremal version of this uniqueness result, we obtain the conjectured mass-angular momentum inequality for multiple dynamical black holes using the main theorem of [17].