Analytical proof of the isospectrality of quasinormal modes for Schwarzschild-de Sitter and Schwarzschild-Anti de Sitter spacetimes

The deep reason why the equations describing axial and polar perturbations of Schwarzschild black holes have the same spectrum is far from trivial. In this article, we revisit the original proof and try to make it clearer. Still focusing on uncharged and non-rotating black holes, we extend the results to spacetimes including a cosmological constant, which have so far mostly been investigated numerically from this perspective.