Null Infinity as a Weakly Isolated Horizon

Abstract

Null infinity arises as a boundary of the Penrose conformal completion of an asymptotically flat physical space-time. We first note that null infinity is a weakly isolated horizon (WIH), and then show that its familiar properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs is very different from that extracted at null infinity. We show that these differences can be directly traced back to the fact that null infinity is a WIH in the conformal completion rather than the physical space-time. In particular, the BMS group at null infinity stems from the symmetry group of WIHs. In a companion paper, we obtain fluxes and charges associated with symmetries associated with both null infinity and black hole (and cosmological) horizons using a new Hamiltonian framework. The fact that is there is a single mathematical framework underlying these different situations paves the way to explore the relation between horizon dynamics in the strong field region and waveforms at infinity. It should also be useful in the analysis of black hole evaporation in quantum gravity.

21 pages. At referee's suggestion version 1 of this paper was split into two papers. Consequently the current version v2 contains only the first three sections of v1. The remaining sections appear in a paper entitled "Null Infinity and Horizons: New Approach to Fluxes and Charges', arXiv:2407.03254. Both papers are at press at Phy. Rev. D

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• Projective path to points at infinity in spherically symmetric spacetimes