The Kerr–Newman–(anti-)de Sitter spacetime: Extremal configurations and electrogeodesics

We study motion of charged test particles, or electrogeodesics, in the Kerr–Newman–(anti-)de Sitter spacetime. We focus on the equatorial plane and the axis of symmetry where the analysis is considerably simpler. The electric charge opens up the possibility of new types of trajectories, particularly stationary points where the particle can remain indefinitely. It also influences the stability of the orbits, which can be interesting from the point of view of observations. We review the basic properties of the spacetime—the structure of its horizons, the extremal cases, the possibility of over-extreme rotation, regions admitting closed timelike curves, and the turnaround radius, among other.