Generalized Coulomb-type interaction embedded in a non-inertial cosmic string spacetime in a slow-rotation limit

Motivated by the great interest in studying quantum and gravitational phenomena in a unified way, scalar bosons are considered in a cosmic string spacetime and in a non-inertial frame, with a generalized Coulomb-type interaction containing both inverse quadratic and inverse cubic corrections. Solutions for this generalized interaction are shown for an arbitrary state in the slow rotation limit in a quasi-exact manner and a discussion is given of the structure of the problem, whose special case appears in the form of a doubly confluent Heun differential equation. The previously known solution for the simplest case of this problem, corresponding to the ordinary Coulomb interaction, is recovered.

💡 Research Summary

The paper investigates relativistic scalar bosons in the spacetime of a cosmic string while simultaneously accounting for non‑inertial (rotating) effects. Starting from the static, cylindrically symmetric metric of a cosmic string, the authors introduce a constant angular velocity ω through the coordinate transformation φ → φ + ωt, obtaining a rotating metric that contains cross‑terms proportional to ω. In the slow‑rotation limit (α ω ≪ 1) the metric simplifies and remains physically admissible for r < 1/(α ω).

The Klein‑Gordon equation for a massive scalar field is written in this background, and separation of variables leads to a radial equation that resembles a Schrödinger equation with an effective potential. The novelty lies in the choice of a generalized Coulomb‑type interaction \