Electromagnetic Field in Higher-Dimensional Black-Hole Spacetimes

A special test electromagnetic field in the spacetime of the higher-dimensional generally rotating NUT-(A)dS black hole is found. It is adjusted to the hidden symmetries of the background represented by the principal Killing-Yano tensor. Such electromagnetic field generalizes the field of charged black hole in four dimensions. In higher dimensions, however, the gravitational back reaction of such a field cannot be consistently solved.