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We give a full analysis of the conservation along null surfaces of generalized energy and supermomenta, for gravitational systems enclosed by a finite boundary. In particular, we interpret the conservation equations in a canonical manner, revealing a notion of symplectic potential and a boundary current intrinsic to null surfaces. This generalizes similar analyses done at asymptotic infinity or on horizons.
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Hopfmüller et al. (2018) studied this question.
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