Black Hole Membrane Paradigm from Boundary Scalar Field

Black hole membrane paradigm suggests to consider the black hole horizon as a fluid membrane. The membrane has a particular energy-momentum tensor which characterizes the interactions with the falling matter. In this paper, we show that we can construct an action from the scalar field on the horizon which can give the same energy-momentum tensor for the membrane. That is, the membrane can be described effectively by the scalar field on it.