  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 \cite{Park:2013iqa} 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 goal to firmly establish the method of
dimensional reduction to a hypersurface of foliation.} We obtain a theory on a
2D plane (the $(t,r)$-plane) and observe that novel and elaborate boundary
effects are crucial for the consistency of the reduction. The reduction leads
to a 2D interacting quantum field theory. We comment on its application to
black hole information physics.
