The stability conjecture for Kerr–de Sitter quasinormal modes

For Kerr--de Sitter parameters $a$, $\Lambda$, and $M$ satisfying

$$\left(1-\frac{\Lambda a^2}{3}\right)^3>9\Lambda M^2,$$

and lying in the shaded region specified by the source, quasinormal modes are complex frequencies $\lambda$ for which there is a nonzero $u(r,\theta,\phi)$ satisfying the separated wave equation and extending smoothly across both horizons. Kerr--de Sitter mode-stability conjecture. Every such $\lambda\ne0$ satisfies $\operatorname{Im}\lambda<0$, and $\lambda=0$ is a simple resonance. Results cited in the source establish this absence of nondecaying modes in some parameter ranges, but not the stated large range.