Angular momentum at null infinity in Einstein-Maxwell theory

TL;DR

This paper investigates angular momentum flux at null infinity in Einstein-Maxwell theory, showing that the radiative degrees of freedom determine the flux when using Wald-Zoupas charges, aligning with the radiative Noether current rather than stress-energy tensor.

Contribution

It demonstrates that the angular momentum flux in Einstein-Maxwell theory is purely radiative when computed via Wald-Zoupas charges, clarifying the role of different conserved currents.

Findings

The Wald-Zoupas charge includes an additional Maxwell term compared to vacuum GR.

The angular momentum flux is determined solely by radiative degrees of freedom.

Maxwell fields contribute through the radiative Noether current, not stress-energy flux.

Abstract

On Minkowski spacetime, the angular momentum flux through null infinity of Maxwell fields, computed using the stress-energy tensor, depends not only on the radiative degrees of freedom, but also on the Coulombic parts. However, the angular momentum also can be computed using other conserved currents associated with a Killing field, such as the Noether current and the canonical current. The flux computed using these latter two currents is purely radiative. A priori, it is not clear which of these is to be considered the true flux of angular momentum for Maxwell fields. This situation carries over to Maxwell fields on non-dynamical, asymptotically flat spacetimes for fluxes associated with the Lorentz symmetries in the asymptotic Bondi-Metzner-Sachs (BMS) algebra. We investigate this question of angular momentum flux in the full Einstein-Maxwell theory. Using the prescription of Wald and Zoupas, we compute the charges associated with any BMS symmetry on cross-sections of null infinity. The change of these charges along null infinity then provides a flux. For Lorentz symmetries, the Maxwell fields contribute an additional term, compared to the Wald-Zoupas charge in vacuum general relativity, to the charge on a cross-section. With this additional term, the flux associated with Lorentz symmetries, e.g., the angular momentum flux, is purely determined by the radiative degrees of freedom of the gravitational and Maxwell fields. In fact, the contribution to this flux by the Maxwell fields is given by the radiative Noether current flux and not by the stress-energy flux.