Scalar perturbations in a Top-Star spacetime

TL;DR

This paper investigates scalar perturbations and particle dynamics in Top-Star spacetime, adapting 4D formalisms to 5D and comparing classical and quantum solution methods, advancing understanding of perturbative effects in exotic spacetimes.

Contribution

It extends the Mano-Suzuki-Takasugi formalism to 5D Top-Star spacetime and compares it with Seiberg-Witten formalism, linking black hole perturbation theory with quantum field theory.

Findings

Successful adaptation of 4D formalism to 5D spacetime.

Comparison between classical and quantum solution methods.

Insights into scalar field evolution and self-force effects.

Abstract

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.