Math Conjectures

Nonlinear Stability of Subextremal Kerr Black Holes

OPENLandmarkConjectureProposed c. 1965 · Canonical special case

Canonical statement

For every fixed Kerr exterior with mass m>0m>0 and angular momentum parameter ∣a∣<m|a|<m, all sufficiently small asymptotically flat vacuum perturbations of compatible initial data have a complete exterior development that, after gauge adjustment, remains close to and asymptotically approaches a nearby Kerr exterior.
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For every fixed Kerr exterior with mass \(m>0\) and angular momentum parameter \(|a|<m\), all sufficiently small asymptotically flat vacuum perturbations of compatible initial data have a complete exterior development that, after gauge adjustment, remains close to and asymptotically approaches a nearby Kerr exterior.
PDE-010:[Hintz2026Kerr][Hintz2026ConstraintDamping][Hintz2026WavesII]
Partial differential equationsMathematical physicsGeometry and topology

Notes

Nonlinear Kerr stability is the rotating-black-hole analogue of the nonlinear stability of Minkowski and Schwarzschild spacetimes. The record fixes each subextremal exterior ∣a∣<m|a|<m, excluding extremal and interior claims. Hintz's June 2026 manuscript and two analytic dependencies state a full theorem at that scope [Hintz2026Kerr] [Hintz2026ConstraintDamping] [Hintz2026WavesII]. Their size and recency require an independent technical audit, so the claim is Grade C rather than an accepted status change.

Proof-claim watch (1)

Full subextremal Kerr exterior stability

Grade C

Substantive full proof claim; not yet independently established.

References (3)

The boxed statement is the canonical open formulation — not a stronger variant or a related research program. The status reflects the catalog's last review; do your own literature search before investing serious effort.