Mass multipoles as horizon surface charges

Determine whether the mass multipoles M_ℓ of an isolated horizon segment can be realized as horizon surface charges associated with natural canonical transformations generated by symmetries, analogous to the angular momentum multipoles.

Background

In the QLH framework, angular momentum multipoles on isolated horizons arise as surface charges for canonical transformations generated by symmetry vector fields, extending the notion of the horizon angular momentum. This provides a clear Hamiltonian interpretation for all higher spin multipoles.

For mass multipoles defined from the isolated horizon geometry (via curvature and rotational 1-form data), a similar Hamiltonian charge interpretation has not been established; the review explicitly notes that it remains unknown whether mass multipoles share this property, motivating a precise question about identifying corresponding canonical generators.