Magnetic field seed generation in plasmas around charged and rotating black holes

Previous work by the authors introduced the possibility of generating seed magnetic fields by spacetime curvature and applied it in the vicinity of a Schwarzschild black hole. It was pointed out that it would be worthwhile to consider the effect in other background geometries and particularly in the vicinity of a rotating black hole, which is generically to be expected, astrophysically. In this paper that suggestion is followed up and we calculate generated magnetic field seed due to Reissner-Nördstrom and Kerr spacetimes. The conditions for the drive for the seed of a magnetic field is obtained for charged black holes, finding that in the horizon the drive vanishes. Also, the ψN-force produced by the Kerr black hole is obtained and its relation with the magnetic field seed is discussed, producing a more effective drive.