Null infinity and horizons: A new approach to fluxes and charges

We introduce a Hamiltonian framework tailored to degrees of freedom (DOF) of field theories that reside in suitable 3-dimensional open regions, and then apply it to the gravitational DOF of general relativity. Specifically, these DOF now refer to open regions $\stackrel{^}{\mathcal{R}}$ of null infinity ${\ensuremath{\mathcal{I}}}^{+}$, and $R$ of black hole (and cosmological) horizons $\mathrm{\ensuremath{\Delta}}$ representing equilibrium situations. At ${\ensuremath{\mathcal{I}}}^{+}$ the new Hamiltonian framework yields the well-known BMS fluxes and charges. By contrast, all fluxes vanish identically at $\mathrm{\ensuremath{\Delta}}$ just as one would physically expect. In the companion paper [Phys. Rev. D 110, 044048 (2024).] we showed that, somewhat surprisingly, the geometry and symmetries of ${\ensuremath{\mathcal{I}}}^{+}$ and $\mathrm{\ensuremath{\Delta}}$ descend from a common framework. This paper reinforces that theme: Very different physics emerges in the two cases from a common Hamiltonian framework because of the difference in the nature of degrees of freedom on ${\ensuremath{\mathcal{I}}}^{+}$ and $\mathrm{\ensuremath{\Delta}}$, discussed in the companion paper. Finally, we compare and contrast this Hamiltonian approach with those available in the literature.