Gyromagnetic ratio of higher dimensional black holes

Abstract

We consider a rotating black hole with two angular momenta in D = 6 dimensions and three angular momenta in D = 7 dimensions. Using Wald's test field approach we derive the solution for the electromagnetic field occurring when the black hole is placed in a uniform magnetic field. It is shown that a weakly charged rotating black hole in D = 6 and 7 dimensions possesses two and three independent magnetic dipole moments, respectively. We conjecture that the gyromagnetic ratio of a D-dimensional weakly charged Myers?Perry black hole possesses the value g = D ? 2.