  We study pure $D$ dimensional Einstein gravity in spacetimes with a generic
null boundary. We focus on the symplectic form of the solution phase space
which comprises a $2D$ dimensional boundary part and a $2(D(D-3)/2+1)$
dimensional bulk part. The symplectic form is the sum of the bulk and boundary
parts, obtained through integration over a codimension 1 surface (null
boundary) and a codimension 2 spatial section of it, respectively. Notably,
while the total symplectic form is a closed 2-form over the solution phase
space, neither the boundary nor the bulk symplectic forms are closed due to the
symplectic flux of the bulk modes passing through the boundary. Furthermore, we
demonstrate that the $D(D-3)/2+1$ dimensional Lagrangian submanifold of the
bulk part of the solution phase space has a Carrollian structure, with the
metric on the $D(D-3)/2$ dimensional part being the Wheeler-DeWitt metric, and
the Carrollian kernel vector corresponding to the outgoing Robinson-Trautman
gravitational wave solution.
