Null infinity as an open Hamiltonian system

TL;DR

The paper reframes Bondi energy as a time-dependent Hamiltonian on the covariant phase space by moving radiative degrees of freedom from the bulk into fixed background data at null infinity. It develops a rigorous bulk-plus-boundary action on a generic null boundary, identifies the gravitational edge modes, and derives the radiative phase space via a double-null foliation and NP-type tetrads to reach null infinity. The authors show how corner terms and boundary symplectic structure render the quasi-local charges integrable, and they reinterpret Bondi energy as the Helmholtz free energy of gravitational edge modes, with the Bondi mass loss law arising from the decrease of this free energy toward equilibrium. This framework provides a concrete, non-perturbative bridge between radiative gravity, boundary dynamics, and potential quantum-gravity boundary theories, suggesting new ways to encode asymptotic data and energy in a boundary-only Hamiltonian picture.

Abstract

When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent Hamiltonian on the covariant phase space. Our derivation starts from the Hamiltonian formulation in domains with boundaries that are null. We introduce the most general boundary conditions on a generic such null boundary, and compute quasi-local charges for boosts, energy and angular momentum. Initially, these domains are at finite distance, such that there is a natural IR regulator. To remove the IR regulator, we introduce a double null foliation together with an adapted Newman--Penrose null tetrad. Both null directions are surface orthogonal. We study the falloff conditions for such specific null foliations and take the limit to null infinity. At null infinity, we recover the Bondi mass and the usual covariant phase space for the two radiative modes at the full non-perturbative level. Apart from technical results, the framework gives two important physical insights. First of all, it explains the physical significance of the corner term that is added in the Wald--Zoupas framework to render the quasi-conserved charges integrable. The term to be added is simply the derivative of the Hamiltonian with respect to the background fields that drive the time-dependence of the Hamiltonian. Secondly, we propose a new interpretation of the Bondi mass as the thermodynamical free energy of gravitational edge modes at future null infinity. The Bondi mass law is then simply the statement that the free energy always decreases on its way towards thermal equilibrium.