  We extend the discussion of the "Kerr/CFT correspondence" and its recent
developments to the more general gauge/gravity correspondence in the full
extremal black hole space-time of the bulk by using a technique of the
holographic renormalization group (RG) flow. It is conjectured that the
extremal black hole space-time is holographically dual to the chiral two
dimensional field theory. Our example is a typical four dimensional
Reissner-Nordstrom black hole, a system in which the M5-brane is wrapped on
four cycles of Calabi-Yau threefold. In five dimensional supergravity view
point this near horizon geometry is $AdS_3\times S^2$, and three dimensional
gravity coupled to moduli fields is effectively obtained after a dimensional
reduction on $S^2$. Constructing the Hamilton-Jacobi equation, we define the
holographic RG flow from the three dimensional gravity. The central charge of
the Virasoro algebra is calculable from the conformal anomaly at the point
where the beta function defined from gravity side becomes zero. In general, we
can also identify the c-function of the dual two dimensional field theory. We
show that these flow equations are completely equivalent to not only BPS but
also non-BPS attractor flow equations of the muduli fields. The attractor
mechanism by which the values of the moduli fields are fixed at the event
horizon of the extremal black hole can be understood equivalently to the fact
that the RG flows are fixed at the critical points in the dual field theory.
