Abstract
It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1,2,3]. 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 \( \mathcal{I} \)+.
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Ashtekar, A., Khera, N., Kolanowski, M. et al. Non-expanding horizons: multipoles and the symmetry group. J. High Energ. Phys. 2022, 28 (2022). https://doi.org/10.1007/JHEP01(2022)028
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DOI: https://doi.org/10.1007/JHEP01(2022)028