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

TL;DR

This paper investigates scalar bosons in a cosmic string spacetime with a generalized Coulomb interaction, deriving solutions in a slow-rotation non-inertial frame and connecting to known Coulomb solutions.

Contribution

It introduces a generalized Coulomb-type interaction in a non-inertial cosmic string spacetime and provides quasi-exact solutions in the slow rotation limit, extending previous Coulomb problem results.

Findings

Derived solutions for the generalized Coulomb interaction in a cosmic string spacetime.

Connected the generalized case to the known Coulomb solution.

Analyzed the differential equation structure, including the doubly confluent Heun form.

Abstract

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.