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We study a speci?c class of black holes which are called extremal. By de?ning extremality asdouble-horizon condition and imposing ?niteness assumption, we show that the dynamics of ?eldsat the horizon decouples from the rest of space. This decoupling occurs by vanishing all radialderivatives. We show this decoupling for the extremal black holes in the theories of gravity correctedby f(R)terms.We also show that these two above conditions leads to AdS × S1 near horizon geometry2of rotating black holes. This geometry which preserve SO(2, 1) × U(1) isometry group, is recentlyused in improving the entropy function method. Finally we show that decoupled equations of horizon can be derived from a...