Shape multipoles as Hamiltonian charges

Identify a phase-space and symmetry framework in which shape multipoles on a dynamical horizon segment arise as Hamiltonian surface charges associated with canonical transformations, paralleling the BMS supermomentum charges at null infinity.

Background

The review highlights a striking functional identity between horizon multipoles and BMS supermomentum/dual supermomentum charges, even in radiative regimes, suggesting deep structural parallels between WIHSs and null infinity.

While BMS charges at null infinity are well-understood within Hamiltonian phase spaces, an analogous interpretation for shape multipoles on DHSs would unify quasi-local and asymptotic observables and clarify symmetry generators acting on horizon data.