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Abstract  We reduce the 4D Einstein‐Hilbert action to a constant‐radius hypersurface of foliation. The resulting theory is a scalar theory defined on a 3D hypersurface of the original black hole background, and has an exponential potential. Once the the hypersurface is located at the Schwarzschild radius, the 3D theory is effectively reduced to a 2D Liouville type theory. We compute the entropy associated with the hypersurface intrinsic degrees of freedom, and show that its leading order reproduces the Bekenstein‐Hawking area law. The subleading terms come in logarithm/inverse powers of the area.

ADM reduction of Einstein action and black hole entropy