Null Infinity and Horizons: A New Approach to Fluxes and Charges

TL;DR

This paper develops a Hamiltonian framework for gravitational degrees of freedom at null infinity and horizons, clarifying fluxes and charges, and highlighting differences between these regions within a unified approach.

Contribution

It introduces a new Hamiltonian approach applicable to open regions of null infinity and horizons, unifying the treatment of fluxes and charges in these contexts.

Findings

BMS fluxes and charges recovered at null infinity.

Fluxes vanish at black hole horizons, aligning with physical expectations.

Unified Hamiltonian framework reveals differences in physics at infinity and horizons.

Abstract

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 of null infinity, and of black hole (and cosmological) horizons representing equilibrium situations. At null infinity the new Hamiltonian framework yields the well-known BMS fluxes and charges. By contrast, all fluxes vanish identically at black hole (and cosmological) horizons just as one would physically expect. In a companion paper we showed that, somewhat surprisingly, the geometry and symmetries of these two physical configurations 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. Finally, we compare and contrast this Hamiltonian approach with those available in the literature.