On symplectic form for null boundary phase space

To formulate gravity in spacetimes bounded by a null boundary, an arbitrary hypothetical surface, boundary degrees of freedom (d.o.f) should be added to account for the d.o.f and dynamics spacetime regions excised behind boundary. In D dimensional example, are labelled charges defined at D-2 spacelike slices While modes can have their own dynamics, interaction with bulk is governed flux-balance equations which may interpreted as diffusion equation describing "dissolution" gravitons into From viewpoint, obey local thermodynamical Our description suggests new "semiclassical" quantization system quantized while classical. This semiclassical treatment relevant questions black hole physics.