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A new procedure for computing electromagnetic fields in curved space-times is presented. With this procedure, the problem is reduced to solving one complex linear scalar wave equation. Many space-times of astrophysical importance may be treated in this manner, including black-hole and neutron-star spaces and cosmological models.

We derive the expression for the electromagnetic field of a point charge at rest on the symmetry axis near a rotating Kerr black hole. This is a generalization of the previously obtained solution for the field of a point charge near a nonrotating Schwarzschild black hole. Unlike the Schwarzschild case the charge is found to give rise to magnetic fields as seen by a stationary or locally nonrotating observer.