Mass and dual mass: A gravitational analogue of the Dirac quantization rule and its physical implications
It is shown that (asymptotically multi-NUT) gravitational magnetic monopoles, which can be described by an \(S^ 3/Z_ N\) principal Hopf- bundle structure at conformal null infinity \((Z_ N\) is a cyclic subgroup of order N of Z), provide a gravitational analogue of the Dirac quantization rule, which involves the total magnetic (dual) mass of the space-time - a measurement of the first Chern class of the bundle - and the mass of a test particle located in the rest frame defined at infinity by the Bondi (or dual Bondi) 4-momentum. It is shown that \(SU_ 2/U_ 1\) preserves the asymptotic structure. A definition of the angular momentum operator which extends that available for test electric charges in the field of a (Maxwellian) Yang- Wu magnetic monopole is presented. The commutation relations are dictated by the quantization rule. Various physical consequences are mentioned. Since \(SU_ 2\) is a double covering of \(SO_ 3\), gravitational magnetic monopoles provide a topological explanation for the existence of particles with half-integer spin. Abelian \((U_ 1)\), non-Abelian \((SU_ 2)\) asymptotic degrees of freedom of the gravitational field could be related to suitable nontrivial cohomology classes; Penrose's nonlinear graviton modes could emerge as self (antiself) adjoint (Yang-Mills) gauge connections.
scientific article; zbMATH DE number 3994495