Charged particle dynamics in singular spacetimes: hydrogenic mapping and curvature-corrected thermodynamics

Abstract

We analyze the dynamics of charged test particles in a singular, horizonless spacetime arising as the massless limit of a charged wormhole in the Einstein--Maxwell--Scalar (EMS) framework. The geometry, sustained solely by an electric charge $Q$, features an infinite sequence of curvature singularity shells, with the outermost at \( r_* = \frac{2|Q|}{\pi} \) acting as a hard boundary for nonradial motion, while radial trajectories can access it depending on the particle charge-to-mass ratio \( |q|/m \). Exploiting exact first integrals, we construct the effective potential and obtain circular orbit radii, radial epicyclic frequencies, and azimuthal precession rates. In the weak-field limit (\( r \gg |Q| \)), the motion reduces to a Coulombic system with small curvature-induced retrograde precession. At large radii, the dynamics maps to a hydrogenic system, with curvature corrections inducing perturbative energy shifts. Approaching \( r_* \), the potential diverges, producing hard-wall confinement. Curvature corrections also modify the spectral thermodynamics, raising energies and slightly altering entropy and heat capacity. Our results characterize the transition from Newtonian-like orbits to strongly confined, curvature-dominated dynamics.