Nonlinear stability of Kerr-de Sitter for all subextremal parameters
In plain words
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.
Precise statement
For Kerr-de Sitter with $\Lambda > 0$ in the full subextremal range, nonlinear stability is proved conditional on mode stability of the linearized gauge-fixed Einstein equation (Hintz, Petersen, Vasy 2025). Prove mode stability for gravitational perturbations of Kerr-de Sitter for all subextremal $(a, M, \Lambda)$, or exhibit a growing mode. An answer is a proof or an explicit unstable mode.
What would settle it
A proof of gravitational mode stability for all subextremal Kerr-de Sitter parameters, which completes the conditional nonlinear theorem.
Status in the literature
Unverified note
Slow rotation proved (Hintz and Vasy 2018); the full range is proved conditional on mode stability (Hintz, Petersen, Vasy, arXiv:2508.06620, 2025); scalar (Klein-Gordon) mode stability for all subextremal parameters was posted by Hintz (arXiv:2608.25868, 2026), and gravitational mode stability is open.