Electrovacuum black-hole uniqueness conjecture
Conjecture: Every asymptotically flat, stationary, axisymmetric solution of the Einstein--Maxwell equations representing a regular electrovacuum black hole is uniquely determined, up to isometry and electromagnetic gauge equivalence, by its global data, including its asymptotic conserved charges. In the connected-horizon case, the unique solution is the Kerr--Newman spacetime, with parameters determined by the mass, angular momentum, and electric and magnetic charges.
References
Primary source
Additional references
- Electrovacuum Black Hole Uniqueness — arXiv — Qing Han, Marcus Khuri, Gilbert Weinstein, Jingang Xiong
Progress summary
A conditional theorem for black holes with several horizons is reported, but the broader conjecture remains unsettled.
The conjecture asks whether stationary, axisymmetric electrovacuum black holes are uniquely determined by their global data. Earlier results handled important connected-horizon cases under strong assumptions.
Known results
- Chruściel and Costa, 2010: uniqueness for rotating, degenerate electrovacuum black holes with a connected horizon, yielding Kerr–Newman.
- 2011 inverse-scattering work: uniqueness of Kerr–Newman for stationary, axisymmetric electrovacuum spacetimes with a connected Killing horizon, including the degenerate case.
- 1996 review: uniqueness was known for connected, non-degenerate, appropriately regular stationary-axisymmetric electrovacuum black holes.
- 2026 work: uniqueness for a specialized type- class with a non-aligned electromagnetic field, not the general conjecture.
September 10, 2026 conditional multi-horizon theorem
Qing Han, Marcus Khuri, Gilbert Weinstein, and Jingang Xiong report a theorem classifying multi-horizon solutions in the stated stationary, axisymmetric setting. It extends singular-harmonic-map methods to electrovacuum, but is conditional on explicit hypotheses and does not settle the full conjecture; the advance is unverified.
Current status (as of September 2026): A conditional multi-horizon uniqueness theorem has been reported, while the general electrovacuum black-hole uniqueness conjecture remains open and the report has not been independently verified.
Solutions 0
No solutions have been posted yet.