Stability and uniqueness of Kerr black holes

7 problems

• Nonlinear fate of perturbed extremal Kerr black holes

  Open

  At maximum spin, small disturbances do not die away at the horizon: some of their derivatives grow forever, an effect found in 2011 by the mathematician Stefanos Aretakis. Whether this growth destroys the extremal black hole in the full theory is unknown.

• Does every generic gravitational collapse settle to Kerr black holes?

  Open

  The final state conjecture says that any isolated system eventually becomes a set of Kerr black holes moving apart plus outgoing gravitational radiation. Stability of a single Kerr black hole covers only the small-disturbance part of this claim.

• Are Kerr-AdS black holes nonlinearly stable with reflecting boundary conditions?

  Open

  In anti-de Sitter space, a model universe with a reflecting boundary, waves cannot escape and may concentrate into ever smaller scales. Even empty anti-de Sitter space is unstable, and the fate of its black holes is unknown.

• Nonlinear stability of Kerr-de Sitter for all subextremal parameters

  Partially resolved

  With a positive cosmological constant, as in our expanding universe, stability is proved for slow spin and is reduced, for all spins, to one remaining check. That check is the absence of exponentially growing modes of the linearized equations, called mode stability.

• Linear stability of Kerr-Newman black holes for all subextremal parameters

  Partially resolved

  The charged, spinning Kerr-Newman solution is the most general black hole of Einstein-Maxwell theory. Its stability has resisted proof because gravitational and electromagnetic waves stay coupled and cannot be separated into simple equations.

• Is Kerr the only smooth stationary vacuum black hole?

  Partially resolved

  The no-hair theorem says a settled black hole is fully described by its mass and spin. The classic proofs assume the spacetime is analytic, a far stronger smoothness condition than physics justifies, and without it the result is proved only near Kerr.

• Nonlinear stability of Kerr for all spins below extremal

  Partially resolved

  Proofs that a spinning black hole is stable appeared only in 2021-2022, and only for slow spin. In June and September 2026 two independent proofs were posted that cover every spin below the maximum, and these await verification.