Mass and dual mass: a gravitational analogue of the Dirac quantization rule and its physical implications.

Details Mass and dual mass: a gravitational analogue of the Dirac quantization rule and its physical implications. Mass and dual mass: a gravitational analogue of the Dirac quantization rule and its physical implications.

Aug 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987gregr..19..809m&link_type=abstract

General Relativity and Gravitation, Volume 19, Issue 8, pp.809-825

Mathematics

Logic

3

Gravitation Theory:Magnetic Monopoles, Magnetic Monopoles:Gravitation Theory, Quantum Gravity

Scientific paper

It is shown that (asymptotically multi-NUT) gravitational magnetic monopoles, which can be described by anS 3/Z N principal Hopf-bundle structure at conformal null infinity (Z N is a cyclic subgroup of orderN ofZ). 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 thatSU 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. SinceSU 2 is a double covering ofSO 3, gravitational magnetic monopoles provide a topological explanation for the existence of particles with half-integer spin. Abelian (U 1), non-AbelianSU 1 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.

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