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

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.

35 pages. At referee's suggestion version 1 of arXiv:2402.17977 was split into two papers. This paper contains slightly expanded versions of the material that was in sections IV and V and Appendix A and B of that submission. Both papers are at press at Phy. Rev. D

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Cited by in corpus (8)

• Null Infinity as a Weakly Isolated Horizon
• Quasi-Local Black Hole Horizons: Recent Advances
• Radiation in Fluid/Gravity and the Flat Limit
• Asymptotic Limit of Null Hypersurfaces
• ADM, BMS, and some puzzling interconnections
• The Operational Meaning of Total Energy of Isolated Systems in General Relativity
• Holographic pressure and volume for black holes
• News tensor on null hypersurfaces