Quasinormal modes and strong cosmic censorship in near-extremal Kerr–Newman–de Sitter black-hole spacetimes

The quasinormal resonant modes of massless neutral fields in near-extremal Kerr–Newman–de Sitter black-hole spacetimes are calculated in the eikonal regime. It is explicitly proved that, in the angular momentum regime $\overline{a}>\sqrt{\frac{1-2\overline{\Lambda }}{4+\overline{\Lambda }/3}}$, the black-hole spacetimes are characterized by slowly decaying resonant modes which are described by the compact formula $\Im \omega \left(n\right)={\kappa }_{+}\cdot (n+\frac{1}{2})$ [here the physical parameters $\{\overline{a},{\kappa }_{+},\overline{\Lambda },n\}$ are respectively the dimensionless angular momentum of the black hole, its characteristic surface gravity, the dimensionless cosmological constant of the spacetime, and the integer resonance parameter]. Our results support the validity of the Penrose strong cosmic censorship conjecture in these black-hole spacetimes.