Electrogeodesics in the di-hole Majumdar-Papapetrou spacetime

TL;DR

This paper analyzes the structure and stability of electrogeodesics around two charged black holes in equilibrium, revealing unique features like multiple angular frequencies for circular orbits, using both analytical and numerical methods.

Contribution

It provides a detailed study of electrogeodesics in the Majumdar-Papapetrou spacetime with two black holes, highlighting novel orbital behaviors not seen in Newtonian gravity.

Findings

Regions with two different angular frequencies for the same orbit radius

Existence of stable and unstable circular electrogeodesics

Differences between weak-field and near-field behaviors

Abstract

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.