Quasinormal modes of near-extremal Reissner-Nordström-de Sitter spacetimes

We study quasinormal modes (QNMs) for the Klein-Gordon equation on Reissner-Nordström-de Sitter black holes with near-extremal charge. We locate all QNMs of size $\mathcal{O}({\kappa }_{\mathrm{C}})$ where ${\kappa }_{\mathrm{C}}$ is the surface gravity of the Cauchy horizon (which vanishes at extremality): they are well-approximated by ${\kappa }_{\mathrm{C}}$ times QNMs of the near-horizon geometry ${\mathrm{A}\mathrm{d}\mathrm{S}}^2\times {\mathbb{S}}^2$ of the extremal limit.