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The covariant Hamiltonian formulation for general relativity is studied interms of self-dual variables on a manifold with an internal and lightlikeboundary. At this inner boundary, new canonical variables appear: a spinor anda spinor-valued two-form that encode the entire intrinsic geometry of the nullsurface. At a two-dimensional cross-section of the boundary, quasi-localexpressions for the generators of two-dimensional diffeomorphisms, timetranslations, and dilatations of the null normal are introduced and written interms of the new boundary variables. In addition, a generalisation of thefirst-law of black-hole thermodynamics for arbitrary null surfaces is found,and the relevance of the framework for non-perturbative quantum gravity isstressed and explained.

New boundary variables for classical and quantum gravity on a null surface