Decoupling and non-decoupling dynamics of large D black holes

The limit of large number of dimensions localizes the gravitational field of a black hole in a well-defined region near the horizon. The perturbative dynamics of the black hole can then be characterized in terms of states in the near-horizon geometry. We investigate this by computing the spectrum of quasinormal modes of the Schwarzschild black hole in the 1 /D expansion, which we find splits into two classes. Most modes are non-decoupled modes : non-normalizable states of the near-horizon geometry that straddle between the near-horizon zone and the asymptotic zone. They have frequency of order D/r 0 (with r 0 the horizon radius), and are also present in a large class of other black holes. There also exist a much smaller number of decoupled modes : normalizable states of the near-horizon geometry that are strongly suppressed in the asymptotic region. They have frequency of order 1 /r 0 , and are specific of each black hole. Our results for their frequencies are in excellent agreement with numerical calculations, in some cases even in D = 4