Dirac equation for spherically symmetric AdS5 spacetime and application to a boson star in EGB gravity

Abstract

We discuss the Dirac equation in a curved 5-dimensional spherically symmetric space-time. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating space-times with equal angular momenta. It has a symmetry SU (2) × U (1) 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 space-time and the space-time of a boson star.

Spinor fields in spherical symmetry: Einstein–Dirac and other space-times

“…Let us choose the curvature radial coordinate u = r in the metric (7) (so that e β = r ), Then, in the general case, the temporal component of the Einstein equations can be presented in the integral form:…”

“…Scattering of a Dirac spinor particle in the field of a Schwarzschild black hole was studied in [6]. The Dirac equation in curved 5D spherically symmetric space-time was studied in [7]. A nonlinear spinor field minimally coupled to Maxwell and Proca fields have been considered in a spherically symmetric space-time [8].…”