Non-Expanding horizons: Multipoles and the Symmetry Group

Understand

It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non-expanding horizons (NEHs).

• 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.
• 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 to define charges and fluxes on NHEs, as well as perturbed NEHs.