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We use the inverse-dimensional expansion to compute analytically thefrequencies of a set of quasinormal modes of static black holes ofEinstein-(Anti-)de Sitter gravity, including the cases of spherical, planar orhyperbolic horizons. The modes we study are decoupled modes localized in thenear-horizon region, which are the ones that capture physics peculiar to eachblack hole (such as their instabilities), and which in large black holescontain hydrodynamic behavior. Our results also give the unstableGregory-Laflamme frequencies of Ricci-flat black branes to two orders higher in1/D than previous calculations. We discuss the limits on the accuracy of theseresults due to the asymptotic but not convergent character of the 1/Dexpansion, which is due to the violation of the decoupling condition at finiteD. Finally, we compare the frequencies for AdS black branes to calculations inthe hydrodynamic expansion in powers of the momentum k. Our results extend upto k^9 for the sound mode and to k^8 for the shear mode.

Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion