1304.0014 (I. Y. Park)

ADM reduction of Einstein action and black hole entropy    [PDF]

I. Y. Park

We carry out ADM reduction of the 4D Einstein-Hilbert action. The resulting theory is a scalar theory defined at a 3D hypersurface of the original black hole background, having 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 partition function of the 2D theory, and show that its leading order entropy is proportional to the area of the horizon of the original black hole. The subleading terms come in logarithm/inverse powers of the area.

View original: http://arxiv.org/abs/1304.0014