Diophantine approximation as Cosmic Censor for Kerr–AdS black holes

Abstract The purpose of this paper is to show an unexpected connection between Diophantine approximation and the behavior waves on black hole interiors with negative cosmological constant $$\Lambda <0$$ Λ < 0 explore consequences for Strong Cosmic Censorship conjecture in general relativity. We study linear scalar perturbations $$\psi $$ ψ Kerr–AdS solving $$\Box _g\psi -\frac{2}{3}\Lambda \psi =0$$ □ g - 2 3 = reflecting boundary conditions imposed at infinity. Understanding Cauchy horizon corresponds a analog problem Censorship. Our main result shows that if dimensionless parameters mass $${\mathfrak {m}} = M \sqrt{-\Lambda }$$ m M angular momentum {a}} a satisfy certain non-Diophantine condition, then arising from generic smooth initial data blow up $$|\psi |\rightarrow +\infty | → + ∞ horizon. proof crucially relies novel resonance phenomenon stable trapping exterior poles interior scattering operator gives rise small divisors problem. stark contrast Reissner–Nordström–AdS (Kehle Commun Math Phys 376(1):145–200, 2020) as well previous work analogous \ge 0$$ ≥ —in both cases such were shown remain bounded. As set {m}}, {\mathfrak {a}}$$ , which we blow-up forms Baire-generic but Lebesgue-exceptional subset all below Hawking–Reall bound. On other hand, Baire-exceptional Lebesgue-generic, bounded |\le C$$ ≤ C . This suggests validity $$C^0$$ -formulation may change spectacular way according notion genericity imposed.