Non-expanding horizons: multipoles and the symmetry group

Abstract

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} of NEHs is a 1-dimensional extension of the BMS group mathfrak{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} ±of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that mathcal{I} ± have a small additional structure that reduces mathfrak{G} to the BMS group mathfrak{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} +.