Almost four decades have passed since the generalization of vacuum Kerr solutions to higher dimensions in the form of Myers-Perry black holes, yet an exact solution generalizing their charged extension (Kerr-Newman) to higher dimensions remains unknown in Einstein-Maxwell theory. Likewise, an exact solution for charged multi-NUT spacetimes in higher dimensions is still missing.
In the first part of my talk, considering the Kerr-Schild class in Einstein-Maxwell theory, I will discuss a "No-Go" result related to the charging of Myers-Perry black holes that we obtained in arXiv:2309.02900. In the second part, I will present a slightly stronger generalization of this "No-Go" result in the context of generalized Kerr-Schild spacetimes, which also addresses the charging of multi-NUT solutions. Time permitting, I will further discuss some of the different classes of solutions identified in our analyses.