Dirac equation for sphercially symmetric $AdS_5$ space-time and application to a boson star in EGB gravity

TL;DR

This paper develops a detailed analysis of the Dirac equation in 5-dimensional spherically symmetric anti-de Sitter space-time, providing analytical and numerical solutions, and applies these to study fermion spectra in EGB gravity and boson star backgrounds.

Contribution

It formulates the Dirac equation in 5D spherically symmetric space-time with symmetry SU(2)×U(1), deriving analytical solutions and applying them to EGB gravity and boson star scenarios.

Findings

Analytical solutions for massless and massive Dirac modes are obtained.

The solutions are expressed using Jacobi polynomials.

Numerical spinor solutions are also provided.

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-Schr\"odinger 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.