Null infinity as a weakly isolated horizon

Null infinity, ${\mathcal{I}}^{+}$, arises as a boundary of the Penrose conformal completion $(\widehat{M},{\widehat{g}}_{ab})$ of an asymptotically flat physical space-time $(M,g_{ab})$. We first note that ${\mathcal{I}}^{+}$ is a weakly isolated horizon (WIH) in $(\widehat{M},{\widehat{g}}_{ab})$, and then show that its familiar geometric properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs $\mathrm{\Delta }$ is very different from that extracted at ${\mathcal{I}}^{+}$. We show that these differences can be directly traced back to the fact that ${\mathcal{I}}^{+}$ is a WIH in the conformal completion rather than the physical space-time. In particular, the BMS group at ${\mathcal{I}}^{+}$ stems from the symmetry group of WIHs. In a companion paper [ Phys. Rev. D 110, 044049 (2024).] we obtain fluxes and charges associated with symmetries associated with ${\mathcal{I}}^{+}$ and $\mathrm{\Delta }$ using a new Hamiltonian framework. The fact that is there is a single mathematical framework underlying $\mathrm{\Delta }$ and ${\mathcal{I}}^{+}$ 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.