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

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.

Figures (10)

• Figure 1: The condition function for the bound-state energy solutions and the corresponding effective potential for the first choice of Rainbow functions. The quantum numbers considered are $N=0$, $l=1$, $m=1$, and $\xi/\varepsilon_p=0.1$, which corresponds to $\alpha_1 \approx - 6.93$.
• Figure 2: Bound-state energies and the corresponding energy shift induced by the Rainbow parameter for different quantum numbers, with $m=1$, in the first choice of Rainbow functions.
• Figure 3: Effective potential for analytical solution of first case of proposed Rainbow functions for quantum numbers $N=0$, $l=2$, $m=1$ and $\xi/\varepsilon_p=0.34$.
• Figure 4: Bound state energies against Rainbow parameters for the first case of proposed Rainbow functions for three different sets of $N$ and $l$ quantum numbers and $m=1$.
• Figure 5: Negative energy spectrum dependent on quantum numbers $N$ and $l$, which take values $\{1,2,3,4\}$, for the case of pure General Relativity (solid tiles) and for different Rainbow parameters $\xi$ (semi-transparent tiles), for the second case of proposed Rainbow functions.