Kerr black hole uniqueness conjecture
Every regular, stationary, asymptotically flat, vacuum black-hole spacetime in four-dimensional general relativity is isometric to a member of the Kerr family, parametrized by mass and angular momentum with . In particular, no such spacetime has more than one horizon component.
References
Primary source
Additional references
- Kerr Black Hole Uniqueness — arXiv
Progress summary
An unrefereed August 2026 claim gives uniqueness under symmetry and vacuum assumptions, but the unrestricted conjecture remains unverified.
The conjecture asks whether Kerr is the unique stationary, asymptotically flat vacuum black-hole geometry, including configurations with multiple horizons. Classical results establish only restricted versions, leaving analyticity, regularity, horizon, or symmetry assumptions in place.
Known results
- Carter, Robinson, Bunting, and Mazur established the classical stationary, asymptotically flat, axisymmetric uniqueness theory.
- A 2008 analytic theorem identifies the connected, non-degenerate-horizon case with Kerr, but does not remove analyticity or non-degeneracy.
- A 2007 smooth local theorem proves Kerr uniqueness only under an additional technical identity.
- Extremal uniqueness was reported for a single degenerate horizon, including the Kerr case.
August 2026 claimed theorem
A newly reported theorem claims uniqueness for axially symmetric, stationary, vacuum configurations with multiple horizons and derives a related mass-angular-momentum inequality. The claim is unrefereed and restricted to those hypotheses, so it does not yet verify the full conjecture.
Current status (as of August 2026): A restricted multi-horizon uniqueness theorem has been claimed, but the full Kerr uniqueness conjecture remains open and the new claim is unverified.
Solutions 0
No solutions have been posted yet.