  We derive a prescription for the phase space of general relativity on two
intersecting null surfaces. The boundary symmetry group is the semidirect
product of the group of arbitrary diffeomorphisms of each null boundary which
coincide at the corner, with a group of reparameterizations of the null
generators. The phase space can be extended by acting with half-sided boosts
that generate Weyl shocks along the initial data surfaces, and it then includes
the relative boost angle between the null surfaces. We compute Wald-Zoupas
gravitational charges and fluxes associated with the boundary symmetries. There
is a two-parameter freedom in the charges corresponding to different choices of
polarization on the phase space, which cannot be eliminated using the
Wald-Zoupas stationarity criterion. We also derive the symmetry groups and
charges for a phase space subspace obtained by fixing the direction of the
normal vectors, and for another subspace obtained by fixing their direction and
normalization. The latter group consists of Carrollian diffeomorphisms.
Specializing to perturbations about stationary event horizons, we determine the
independent dynamical degrees of freedom by solving the constraint equations
along the horizons. We mod out by the degeneracy directions of the
presymplectic form, and apply a similar procedure for weak non-degeneracies, to
obtain the horizon edge modes and the Poisson structure. We show that the area
operator of the black hole generates a shift in the relative boost angle under
the Poisson bracket.
