Kerr-Newman black hole in a Melvin-swirling universe

We present a new exact solution of Einstein-Maxwell field equations which represents a rotating black hole with both electric and magnetic charges immersed in a universe which itself is also rotating and magnetized, i.e. the dyonic Kerr-Newman black hole in a Melvin-swirling universe. We show that the solution is completely regular and free of any type of singularity; then we analyze its physical properties, such as the ergoregions and the shape of the event horizons. Finally we present the extremal near horizon geometry of the metric and study its entropy via the Kerr/CFT correspondence.