Charged rotating black holes at large D

We study odd dimensional charged equally rotating black holes in the Einstein-Maxwell theory with/without a cosmological constant by using the large D expansion method, where D is a spacetime dimension. Solving the Einstein-Maxwell equations in the 1/D expansion we obtain the large D effective equations for charged equally rotating black holes. The effective equations describe the nonlinear dynamics of charged equally rotating black holes. Especially the perturbation analysis of the effective equations gives analytic formula for quasinormal mode frequencies, and we can show charged equally rotating black holes have instabilities. As one interesting feature of instabilities, we observe that the ultraspinning instability of neutral equally rotating black holes in de Sitter is connected with the instability of de Sitter Reissner-Nordstrom black hole in a rotation-charge plane of the solution parameter space. So these instabilities have same origin as dynamical properties of charged rotating black holes. We also give perturbation analysis by a small charge for even dimensional equally rotating black holes.