We investigate the (electro-)geodesic structure of the Majumdar-Papapetrou solution representing static charged black holes in equilibrium. We assume only two point sources, imparting thus the spacetime axial symmetry. We study electrogeodesics both in and off the equatorial plane and explore the stability of circular trajectories via geodesic deviation equation. In contrast to the classical Newtonian situation, we find regions of spacetime admitting two different angular frequencies for a given radius of the circular electrogeodesic. We look both at the weak-and near-field limits of the solution. We use analytic as well as numerical methods in our approach.

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Abstract. We investigate the properties of a static, cylindrically symmetric MajumdarPapapetrou-type solution of Einstein-Maxwell equations. We locate its singularities, establish its algebraic type, find its asymptotic properties and weak-field limit, study the structure of electrogeodesics, and determine the mass and charge of its sources. We provide an interpretation of the spacetime and discuss the parameter appearing in the metric.

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