Scalar perturbations in a Top-Star spacetime

We discuss the dynamics of a (neutral) test particle in Topological Star spacetime undergoing scattering processes by a superposed test radiation field, a situation that in a 4D black hole spacetime is known as relativistic Poynting-Robertson effect, paving the way for future studies involving radiation-reaction effects. Furthermore, we study self-force-driven evolution of a scalar field, perturbing the Top-Star spacetime with a scalar charge current. The latter for simplicity is taken to be circular, equatorial and geodetic. To perform this study, besides solving all the self-force related problem (regularization of all divergences due to the self-field, mode sum regularization, etc.), we had to adapt the 4D Mano-Suzuki-Takasugi formalism to the present 5D situation. Finally, we have compared this formalism with the (quantum) Seiberg-Witten formalism, both related to the solutions of a Heun Confluent Equation, but appearing in different contexts in the literature, black hole perturbation theory the first, quantum curves in super-Yang-Mills theories the second.