Approach to the extremal limit of the Schwarzschild–de Sitter black hole

The quasinormal-mode spectrum of the Schwarzschild–de Sitter black hole is studied in the limit of near-equal black-hole and cosmological radii. It is found that the mode frequencies agree with the Pöschl-Teller approximation to one more order than previously realized, even though the effective potential does not. Whether the spectrum approaches the limiting one uniformly in the mode index is seen to depend on the chosen units (to the order investigated). A perturbation framework is set up in which these issues can be studied to higher order in the future.