Dimensional reduction to hypersurface of foliation

Abstract

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.