Scalar Bosons with Coulomb Potentials in a Space with Dual Topological Defects in Rainbow Gravity

TL;DR

This paper investigates how scalar bosons behave in a spacetime with topological defects and energy-dependent gravity modifications, revealing effects on their energy spectrum and bound states.

Contribution

It introduces a unified analysis of scalar bosons in a spacetime with cosmic string, monopole, and rainbow gravity effects, deriving the energy spectrum and examining the influence of rainbow functions.

Findings

Rainbow gravity modifies the scalar boson energy spectrum.

Topological defects affect bound state energies.

Results recover known physics in the appropriate limits.

Abstract

This work studies the relativistic quantum dynamics of scalar bosons in a spacetime containing both a cosmic string and a global monopole within the framework of Rainbow Gravity. An effective metric is constructed to describe the combined topological defects together with the energy-dependent deformation of spacetime. The Klein-Gordon equation is formulated in this background, including scalar, vector, and nonminimal couplings, and its solutions are obtained by separation of variables. Generalized Coulomb-type interactions are considered, allowing a unified analysis of scattering and bound states. The bound-state spectrum is determined from the poles of the corresponding $S$-matrix. Two specific choices of rainbow functions are examined, and their influence on the energy spectrum is analyzed through numerical calculations and, in suitable limits, analytical approximations. The results show how the interplay between topological defects and rainbow gravity corrections affects the spectral properties of scalar bosons, while known results are consistently recovered in appropriate limits.