Null Conservation Laws for Gravity

TL;DR

This paper analyzes conservation laws along null surfaces in gravitational systems, introducing a canonical interpretation with symplectic potential and boundary currents, extending previous analyses at infinity or horizons.

Contribution

It provides a comprehensive framework for null surface conservation laws in gravity, including a canonical interpretation with symplectic structures and boundary currents.

Findings

Conservation equations are interpreted canonically on null surfaces.

Introduces symplectic potential and boundary current concepts.

Generalizes previous analyses at infinity and horizons.

Abstract

We give a full analysis of the conservation along null surfaces of generalized energy and super-momenta, 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.