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

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, mⱼ and mₛ, where n is the radial quantum number, mⱼ is the total magnetic quantum number, mₛ is the spin magnetic quantum number, and explicitly depends on the rainbow functions F(ξ) and G(ξ), curvature parameter α, cosmological constant Λ, fixed radius r₀, and on the rest energy m₀, and z-momentum pz. So, analyzing this spectrum according to the values of mⱼ and mₛ, we see that for mⱼ>0 with mₛ=-1/2 (positive angular momentum and spin down), and for mⱼ<0 with mₛ=+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 Λ, r₀, and α for three different values of n (ground state and the first two excited states).