The symplectic potential for leaky boundaries

TL;DR

This paper introduces a novel method for defining finite symplectic potentials at leaky boundaries in spacetimes, applicable to Einstein-Hilbert gravity, without relying on specific boundary conditions, thus enabling better handling of boundary charges.

Contribution

It proposes a boundary-agnostic approach to symplectic potentials suitable for leaky boundaries, addressing divergence issues in gauge charge definitions.

Findings

Finite symplectic potential for Einstein-Hilbert gravity with leaky boundaries

Identification of two new corner symplectic pairs related to gauge relaxation

Method applicable without specific boundary conditions

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.