Free motion around black holes with discs or rings: between integrability and chaos -- V

Understand

Complete integrability of geodesic motion, the well known feature of the fields of isolated stationary black holes, can easily be "spoilt" by the presence of some additional source (even if highly symmetric).

• In previous papers, we used various methods to show how free time-like motion becomes chaotic if the gravitational field of the Schwarzschild black hole is perturbed by that of a circular disc or ring, considering specifically the inverted first disc of the Morgan-Morgan counter-rotating family and the Bach-Weyl ring as the additional sources.
• The present paper focuses on two new points.
• First, since the Bach-Weyl thin ring is physically quite unsatisfactory, we now repeat some of the analysis for a different, Majumdar-Papapetrou--type (extremally charged) ring around an extreme Reissner-Nordstr\"om black hole, and compare the results with those obtained before.