Curvature Corrections to the Yukawa Potential in Tolman Metrics

Abstract: This work investigates curvature-induced modifications to the Yukawa potential in static, spherically symmetric spacetimes described by Tolman metrics, focusing on their implications for compact stellar objects, with particular application to solutions IV and VI. Motivated by the interplay of quantum interactions and strong gravitational fields in systems like neutron stars, we derive explicit corrections to the Yukawa potential for these metrics. Contrary to previous findings suggesting that curvature corrections break the radial symmetry of the interacting potential near a highly charged black hole, we demonstrate that Tolman metric corrections preserve this symmetry in the local inertial frame. Numerical estimates for astrophysical objects reveal energy shifts of the order of $10^{-34}$ MeV for solution IV. The Tolman VI solution, while singular at the center, yields comparable corrections for most of the fluid sphere radius. A detailed analysis of the repulsive or attractive nature of these curvature corrections for a local observer is provided for each scenario. These results highlight the role of spacetime geometry in shaping quantum interactions and provide a foundation for future studies of nuclear interactions within the context of relativistic stars.