Charges and fluxes on (perturbed) non-expanding horizons

In a companion paper [1] we showed that the symmetry group G of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group B at I+. For each infinitesimal generator of G, we now define a charge and a flux on NEHs as well as perturbed NEHs. The procedure uses the covariant phase space framework in presence of internal null boundaries N along the lines of [2-6]. However, N is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of G are free of physically unsatisfactory features that can arise if N is allowed to be a general null boundary. In particular, all fluxes vanish if N is an NEH, just as one would hope; and fluxes associated with symmetries representing 'time-translations' are positive definite on perturbed NEHs. These results hold for zero as well as non-zero cosmological constant. In the asymptotically flat case, as noted in [1], I-+/- are NEHs in the conformally completed space-time but with an extra structure that reduces G to B. The flux expressions at N reflect this synergy between NEHs and I+. In a forthcoming paper, this close relation between NEHs and I+ will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at I+.