Electromagnetic field in higher-dimensional black-hole spacetimes

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