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A bstract In a companion paper [1] we showed that the symmetry group $$ \mathfrak{G} $$ G of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group $$ \mathfrak{B} $$ B at $$ \mathcal{I} $$ I + . For each infinitesimal generator of $$ \mathfrak{G} $$ 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 $$ \mathcal{N} $$ N along the lines of [2–6]. However, $$ \mathcal{N} $$ N is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of $$ \mathfrak{G} $$ G are free of physically unsatisfactory features that can arise if $$ \mathcal{N} $$ N is allowed to be a general null boundary. In particular, all fluxes vanish if $$ \mathcal{N} $$ 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], $$ \mathcal{I} $$ I ± are NEHs in the conformally completed space-time but with an extra structure that reduces $$ \mathfrak{G} $$ G to $$ \mathfrak{B} $$ B . The flux expressions at $$ \mathcal{N} $$ N reflect this synergy between NEHs and $$ \mathcal{I} $$ I + . In a forthcoming paper, this close relation between NEHs and $$ \mathcal{I} $$ I + will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at $$ \mathcal{I} $$ I + . 

A bstract It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1–3]. In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature [4]. We then show that the symmetry group $$ \mathfrak{G} $$ G of NEHs is a 1-dimensional extension of the BMS group $$ \mathfrak{B} $$ B . These symmetries are used in a companion paper [5] to define charges and fluxes on NEHs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that $$ \mathcal{I} $$ I ± of asymptotically flat space-times are NEHs in the conformally completed space-time . Forthcoming papers will (i) show that $$ \mathcal{I} $$ I ± have a small additional structure that reduces $$ \mathfrak{G} $$ G to the BMS group $$ \mathfrak{B} $$ B , and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at $$ \mathcal{I} $$ I + . 

Recently it was shown that, in an effective description motivated by loop quantum gravity, singularities of the Kruskal space-time are naturally resolved \cite{aoslett,aos}. In this note we explore a few properties of this quantum corrected effective metric. In particular, we (i) calculate the Hawking temperature associated with the horizon of the effective geometry and show that the quantum correction to the temperature is completely negligible for macroscopic black holes, just as one would hope; (ii) discuss the subtleties associated with the asymptotic properties of the space-time metric, and show that the metric is asymptotically flat in a precise sense; (iii) analyze the asymptotic fall-off of curvature; and, (iv) show that the ADM energy is well-defined (and agrees with that determined by the horizon area), even though the curvature falls off less rapidly than in the standard asymptotically flat context.