Dirac equation for sphercially symmetric $Ad{S}_5$ space-time 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 $SU(2)\times U(1)$ 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.

arXiv comment15 pages, 5 figures

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Cited by in corpus (1)

• Spinor fields in spherical symmetry. Einstein-Dirac and other space-times