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tokens: → ∞. This arises from the fact that the gravitational restoring force contains an imaginary component, which acts as an anti-damping (growth) term and dominates the Chandrasekhar dynamical friction when the angular velocity is sufficiently large. Order-of-magnitude estimates for the various time-scales (damping and oscillation) were computed, and their ramifications in the context of this rotating system were explored. We also demonstrated a formal equivalence between Eddington black hole accretion and dynamical friction, thereby ensuring that both these problems can be treated in a unified manner. Through a comparison of the time-scales, it was shown that the Eddington accretion time-scale is faster in some instances, thereby constituting the more dominant effect. However, as black holes cannot accrete matter in such a fashion indefinitely, the limitations of this paradigm were also duly indicated. We have discussed some of the limitations of our formalism in Sections 1 and 5 , since some of the inherent assumptions are not accurate over the entire domain of the galaxy. However, it may be possible to use some of the results obtained herein to study the dynamics near the Galactic Centre (Genzel et al. 2010 ). For instance, recent numerical simulations of supermassive black hole binaries, with Galactic rotation taken into account, suggest that they can be significantly displaced from the Galactic Centre (Awais Mirza et al. 2017 ). Hence, the formalism developed in this paper may provide a heuristic explanation for such phenomena (although we have considered only single black holes in our analysis). Additionally, as the solutions obtained are analytical in nature, the main purpose of the paper is to arguably provide a benchmark solution against which numerical simulations can be compared. Lastly, we note that our treatment is quite general as it is Newtonian in nature, and does not invoke any of the specific features of black holes – it is equally applicable to a massive object in a sea of light particles. For instance, it may be possible to consider Saturn as our massive object, and the (moonlets that constitute) rings of Saturn as the lighter particles, analogous to the works of Griv et al. ( 2000 ) and Griv, Gedalin Yuan ( 2003 ). Moreover, it might be possible to also model axisymmetric systems via this formalism, in the regimes specified herein, such as discs with a Miyamoto–Nagai gravitational potential (Miyamoto Nagai 1975 ). By employing the same mathematical methods employed herein, we can also model the dynamics of a Reissner–Nordström (charged) black hole interacting with a constant galactic magnetic field via the Lorentz force. APPENDIX A: DYNAMICAL FRICTION IN A ROTATING ISOTROPIC CLUSTER Consider a cluster described by a potential–density pair together with an ergodic distribution function (DF) . If we introduce an overall rotation to the cluster, then it was argued in Lynden-Bell ( 1967 ) that the new DF can be obtained by the