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When the bulk spacetime has a foliation structure, the collective dynamics of the hypersurfaces should reveal certain aspects of the bulk physics. The procedure of reducing the bulk to a hypersurface, called ADM reduction, was implemented in [3] where the 4D Einstein‐Hilbert action was reduced along the radial reduction. In this work, reduction along the angular directions is considered with a main...
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...
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