The symplectic potential for leaky boundaries

TL;DR

The paper addresses divergences in charges for gravity with leaky boundaries by exploiting the intrinsic ambiguity of the presymplectic potential and constructing a finite, bulk-based Theta tilde that remains valid regardless of a prescribed boundary Lagrangian.Applied to four-dimensional Einstein–Hilbert gravity in the partial Bondi gauge, the method yields a finite symplectic potential for unconstrained boundary data and reveals two new corner symplectic pairs arising from relaxing the gauge, with a careful treatment of Lambda=0 and Lambda≠0 cases.The work provides a concrete, gauge-friendly framework for open gravitational systems, clarifies the structure of boundary and corner degrees of freedom, and paves the way for further exploration of off-shell symmetries and variational formulations in leaky spacetimes.

Abstract

Charges associated with gauge symmetries are defined on boundaries of spacetimes. But these constructions typically involve divergent quantities when considering asymptotic boundaries. Different prescriptions exist to address this problem, based on ambiguities in the definition of the symplectic potential. We propose a method well suited to leaky boundaries, which describe spacetimes than can exchange matter or radiation with their environment. The main advantage of this approach is that it relies only on the bulk Lagrangian and it is not tied to a specific choice of boundary conditions. The prescription is applied to four dimensional Einstein-Hilbert gravity in the partial Bondi gauge. This leads to a finite symplectic potential for unconstrained boundary data and reveals two new corner symplectic pairs associated with the relaxation of the gauge.