Testing Shannon entropic measurement of the Dirac oscillator under cosmic string geometry

This study delves into the behavior of relativistic fermions in the presence of a topological defect modeled by a rotating cosmic string, with a focus on the Dirac oscillator interaction. The research constructs the background geometry and derives the quantized energy spectrum, which depends on physical and topological parameters. Shannon entropy is employed to analyze the probability density of the ground state, providing a measure of spatial localization and quantum uncertainty. The study reveals how space-time rotation influences the informational content of the Dirac oscillator, offering new insights into the interplay between quantum information and curved space-time. The results demonstrate that the energy spectrum and Shannon entropy are significantly affected by the topological defect parameter and the rotation of the cosmic string, highlighting the complex interplay between geometry and quantum information. The analysis also confirms the consistency of the numerical results with the entropic uncertainty principle, reinforcing the physical interpretation of the findings. Overall, this research provides a deeper understanding of the quantum information landscape in relativistic systems and paves the way for future investigations into entanglement and Fisher information in curved backgrounds.