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). 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. They have physically attractive properties. Finally, it is generally not appreciated that ${\mathcal{I}}^{\pm }$ of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that ${\mathcal{I}}^{\pm }$ 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 ${\mathcal{I}}^{+}$.

31 pages, 2 figures. Some clarifications and references added. Published in JHEP. Typos corrected in Section 2.2 and 2.3.1

References in corpus (5)

• The Weyl BMS group and Einstein's equations
• Introduction to dynamical horizons in numerical relativity
• Symmetric non-expanding horizons
• Tidal deformation of dynamical horizons in binary black hole mergers
• Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric

Cited by in corpus (5)

• Energy scales and black hole pseudospectra: the structural role of the scalar product
• Carrollian hydrodynamics from symmetries
• Pseudospectrum and binary black hole merger transients
• A generalization of the quadruple formula for the energy of gravitational radiation in de Sitter spacetime
• Symmetries of the asymptotically de Sitter spacetimes