Establish the global equivalence of quasilocal and asymptotic energetics

Establish, for the rotating self-gravitating split-monopole Blandford–Znajek engine, whether the quasilocal horizon mass and angular momentum equal the ADM mass and angular momentum, and whether the energy extracted from the horizon equals the energy received by the jet at null infinity, by incorporating the current-sheet boundary term, disk boundary, exterior wind, controlled light-cylinder matching, and Bondi flux.

Background

The paper distinguishes the quasilocal horizon quantities M_H, J_H, and E_extrH from the asymptotic quantities M_ADM, J_ADM, and E_jet∞. In the split-monopole configuration, the hemispheric magnetic flux is supported by an equatorial current sheet rather than being a globally conserved magnetic charge, and the rotating engine has nonstandard near-zone asymptotics.

Consequently, the horizon energy balance derived in the paper does not by itself determine the energy delivered to infinity. A global Hamiltonian or covariant-phase-space treatment must account for the current sheet, any disk completion, electromagnetic energy stored outside the horizon, exterior dissipation, interaction and boundary terms, as well as matching through the light cylinder and the Bondi flux at null infinity.

References

Because Wang's extracting solution is a slow-rotation, quasistationary expansion with nonstandard near-zone asymptotics, neither $M_H=M_{\rm ADM}$ nor $E_{\rm extr}{H}=E_{\rm jet}{\infty}$ follows automatically. Establishing those equalities requires the current-sheet boundary term, a controlled matching across the light cylinder, and the Bondi flux at null infinity.

— Irreducible-Mass Growth and Extractable Energy in a Self-Gravitating Blandford-Znajek Engine  (2609.01534 - Ruffini et al., 1 Sep 2026) in Discussion; see also Section “Quasilocal versus global mass,” Eqs. (en) and (globalmass)