Dirac monopoles on Kerr black holes: Comparing gauges (Q2710979)

This article studies Dirac monopoles on Kerr black holes. The monopoles arise via topologically inequivalent configurations of complex massless scalar fields on a Kerr spacetime. Two possible inequivalent gauges for connections in complex line bundles, the Dirac monopoles are compared. The masses of the monopoles follow from the energy-momentum tensor. The gravitational radius of the black hole is much bigger than the Compton wave length of the monopoles. The masses increase with the square of the Chern number \(n\) of the underlying bundle, but the cases of large \(n\) seem to be suppressed or absent. To get a finite total mass of the monopoles, zeta-function regularization is used which leads to a vanishing total mass. The Hawking radiation on a Schwarzschild background is increased in one gauge whereas it diverges in the second gauge. An explanation of the fact that different gauges lead to different and even infinite results for the Hawking radiation is not provided.