Abstract
We discuss the Dirac equation in a curved 5-dimensional spherically symmetric spacetime. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating spacetimes with equal angular momenta. It has a symmetry [Formula: see text] and is implemented by the Wigner functions. The radial part forms a Dirac–Schrödinger type equation, and existence of the analytical solutions of the massless and the massive modes is confirmed. The solutions are described by the Jacobi polynomials. Also, the spinor of the both large and small components is obtained numerically. As a direct application of our formulation, we evaluate the spectrum of the Dirac fermion in Einstein–Gauss–Bonnet spacetime and the spacetime of a boson star.
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