New Attractors, Entropy Function and Black Hole Partition Function

By making use of the entropy function formalism we study the generalized attractor equations in the four dimensional N=2 supergravity in the presence of higher order corrections. This result might be used to understand a possible ensemble one could associate to an extremal black hole. Using the generality and simplicity of this formalism we establish a duality between a four gravitational theory on AdS_2\times S^2 background and the extremal black hole of the theory whose near horizon geometry it fixed by the AdS_2 background. In this sense the attractor mechanism plays the rule of decoupling limit in the context of AdS/CFT correspondence