Exact solution of the Pauli equation in the presence of a magnetic field in a spinning cosmic string spacetime

We study the Landau quantization of a spin-1/2 charged particle in the background of a spinning cosmic string, using the Pauli equation. The interaction between the particle’s spin, the magnetic field, and spacetime rotation leads to different radial equations for each component of the Pauli spinor. As a result, the upper and lower spinor components differ, each associated with its own principal quantum number and effective angular momentum. The effective angular momentum is influenced by the magnetic field, cosmic string, space rotation and spin. By analyzing a particular case where the eigenenergies are independent of the spin orientation, we find that the magnetic field must be quantized. These eigenenergies reflect both spin–magnetic field interaction and the influence of spacetime rotation. We examine an asymptotic case between angular momentum and the rotation of space, and we also present a graphical analysis of the magnetic field and the energy levels, comparing cases with and without an internal structure for the cosmic string.