We calculate the self-force acting on a charged particle on a circular geodesic orbit in the equatorial plane of a rotating black hole. We show by direct calculation that the dissipative self-force balances with the sum of the flux radiated to infinity and through the black hole horizon. Prograde orbits are found to stimulate black hole superradiance, though we confirm that the condition for floating orbits cannot be met. We calculate the conservative component of the self-force by application of the mode sum regularization method, and we present a selection of numerical results. We obtain the leading-order coefficients in post-Newtonian expansions of the dissipative and conservative components of the self-force, using an analytical method and numerical fitting, respectively. The self-force on the innermost stable circular orbits of the Kerr spacetime is calculated, and comparisons are drawn between the electromagnetic and gravitational self forces.

• Received 23 September 2020
• Revised 28 May 2022
• Accepted 8 July 2022

DOI:https://doi.org/10.1103/PhysRevD.106.024024