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Near Horizon Extreme Magnetized Kerr Geometry

The conjectured magnetized Kerr/CFT correspondence states that the quantum theory of gravity in the near horizon of extreme Kerr black holes immersed by the magnetic field, Near Horizon Extreme Magnetized Kerr black holes, is holographic dual to a two-dimensional chiral conformal field theory. To obtain Near Horizon Extreme Magnetized Kerr geometry, the extreme limit of the magnetized Kerr metric is taken so, $ a=M $ and then continued by transforming the coordinates to have a warped and twisted product of $ \textrm{AdS}_2 \times \textrm{S}^2 $, and also with the Near Horizon Extreme Kerr metric one. Consequently, we can obtain also the new Ernst potentials for those geometries. Finally, the transformed central charge from the extremal non-magnetized one to the magnetized one in the Ernst-Papapetrou formalism is obtained.