A new study has proven the black hole uniqueness conjecture within the context of stationary, axially symmetric, vacuum configurations. Specifically, it has been shown that no regular asymptotically flat configuration can exist with more than one horizon component if every degenerate component possesses non-zero angular momentum. This result is crucial for the theoretical understanding of black holes, as it establishes fundamental limits on their possible structure in astrophysical scenarios.

The proof relies on a refined asymptotic analysis of the associated singular harmonic maps, complemented by a global bound for the Weyl conformal factor. This factor arises from a differential inequality related to scalar curvature. The authors demonstrated that, in any such multi-horizon configuration, the logarithmic angle defect along every finite axis rod is strictly negative, implying that the interaction force along such axis rods is always attractive.

As a corollary of this uniqueness proof in its extremal version, the study also addresses the conjectured mass-angular momentum inequality for multiple dynamical black holes. This result is obtained by utilizing a previous main theorem, reinforcing the consistency of the theory. The uniqueness of Kerr black holes is a fundamental pillar in general relativity, and this demonstration extends its validity to more complex configurations, with direct implications for black hole models in binary or higher-multiplicity systems.