Spacetime curvature corrections for the Yukawa potential and its application for the Reissner-Nordström metric

In this paper, we investigate the influence of the spacetime curvature on the Yukawa potential, focusing on boson-boson interactions derived from the ϕ 3 theory. Using the Bunch-Parker propagator expansion within Born's first approximation, we derive a Yukawa-like potential in a curved spacetime. We analyze the impact of the curvature on the propagator in momentum space, revealing modifications to the potential and showing that the corrections are determined by geometric quantities from Einstein's equations, like the Ricci scalar and tensor. We illustrate this using the Reissner-Nordström metric, highlighting the corrections' magnitude for specific parameters. Our results underscore the nuanced interplay between spacetime curvature and quantum interactions, providing insights into nucleon-nucleon systems in curved spacetimes or near strong gravitational fields.