Null Conservation Laws for Gravity

TL;DR

This paper develops a canonical, intrinsic framework for gravity on finite null boundaries, recasting the Einstein equations on a null hypersurface as a conservation law for a boundary current and a gravitational flux. It introduces an intrinsic symplectic potential on the null boundary that depends only on boundary geometry, fixes the associated ambiguities, and derives a Noether charge that matches a covariant boundary current up to total derivatives. The authors identify three canonical gravity momentum pairs on the null boundary—spin-2 (densitized shear, conformal metric), spin-1 (twist, null generator), and spin-0 (area form, spin-0 momentum mu)—with mu interpreted as a boundary pressure and connected to a generalized Raychaudhuri/Damour dynamics. They also analyze Hamiltonian generators for null boundary symmetries, discuss necessary boundary conditions, and highlight implications for edge modes, null thermodynamics, and potential links to soft theorems.

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.