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

In a magnetized three-dimensional Bonnor-Melvin spacetime with 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 electrody- namics. The resulting equation provides a non-perturbative second-order wave equation that govers the relative motion of the interacting pair. Remarkably, we find exact solubility when considering the interaction as short-range. Consequently, 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.