Dirac fermions under rainbow gravity effects in the Bonnor-Melvin-Lambda spacetime

TL;DR

This paper investigates the energy spectrum of Dirac fermions in a curved spacetime influenced by rainbow gravity, revealing how quantum numbers and spacetime parameters affect the quantized energy levels.

Contribution

It provides a novel analysis of Dirac fermions under rainbow gravity effects in Bonnor-Melvin-Lambda spacetime, deriving the energy spectrum with boundary conditions and exploring parameter influences.

Findings

Energy spectrum depends on rainbow functions, curvature, cosmological constant, and boundary conditions.

Spectrum exhibits symmetry for specific quantum number configurations.

Graphical analysis shows how parameters influence energy levels across states.

Abstract

In this paper, we study the relativistic energy spectrum for Dirac fermions under rainbow gravity effects in the $(3+1)$-dimensional Bonnor-Melvin-Lambda spacetime, where we work with the curved Dirac equation in cylindrical coordinates. Using the tetrads formalism of General Relativity and considering a first-order approximation for the trigonometric functions, we obtain a Bessel equation. To solve this differential equation, we also consider a region where a hard-wall confining potential is present (i.e., some finite distance where the radial wave function is null). In other words, we define a second boundary condition (Dirichlet boundary condition) to achieve the quantization of the energy. Consequently, we obtain the spectrum for a fermion/antifermion, which is quantized in terms of quantum numbers $n$, $m_j$ and $m_s$, where $n$ is the radial quantum number, $m_j$ is the total magnetic quantum number, $m_s$ is the spin magnetic quantum number, and explicitly depends on the rainbow functions $F(\xi)$ and $G(\xi)$, curvature parameter $\alpha$, cosmological constant $\Lambda$, fixed radius $r_0$, and on the rest energy $m_0$, and $z$-momentum $p_z$. So, analyzing this spectrum according to the values of $m_j$ and $m_s$, we see that for $m_j>0$ with $m_s=-1/2$ (positive angular momentum and spin down), and for $m_j<0$ with $m_s=+1/2$ (negative angular momentum and spin up), the spectrum is the same. Besides, we graphically analyze in detail the behavior of the spectrum for the three scenarios of rainbow gravity as a function of $\Lambda$, $r_0$, and $\alpha$ for three different values of $n$ (ground state and the first two excited states).