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Dirac equation for spherically symmetric AdS\(_5\) spacetime and application to a boson star in EGB gravity. (English) Zbl 1371.83169

Summary: 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 \(SU(2)\times U(1)\) 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 spacetime and the spacetime of a boson star.

MSC:

83E15 Kaluza-Klein and other higher-dimensional theories
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
35Q41 Time-dependent Schrödinger equations and Dirac equations
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
85A15 Galactic and stellar structure
81V17 Gravitational interaction in quantum theory
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