Thermodynamic properties of an interacting fermion-antifermion pair in a magnetized spacetime with a non-zero cosmological constant

Abstract

In a magnetized three-dimensional Bonnor-Melvin spacetime with a non-zero cosmological constant, we explore the dynamics of a fermion-antifermion pair interacting through an attractive Coulomb potential. To analyze the relativistic behavior, we seek an analytical solution for the fully covariant two-body Dirac equation derived from quantum electrodynamics. The resulting equation provides a second-order wave equation that governs the relative motion of the interacting pair. Obtaining an exact solution to this wave equation seems not possible; however, we notice solubility, especially when we consider particles to be closely spaced, meaning as the distance between them approaches zero. At that rate, we determine the energy eigenvalues and wave functions utilizing well-known special functions. By employing these solutions, we determine the thermal properties of this system. Despite the divergence observed in the partition function, we effectively tackle this issue by applying a regularization technique based on the mathematical zeta Hurwitz function. This method facilitates the computation of various thermal quantities, such as free energy, total energy, entropy function, and specific heat. Consequently, we provide an in-depth analysis of the thermodynamic characteristics of the system under consideration.