Spacetime curvature corrections for the Yukawa potential and its application for the Reissner-Nordstr\"om Metric

TL;DR

This paper derives how spacetime curvature modifies the Yukawa potential, using the Reissner-Nordström metric as a case study, revealing geometric influences on quantum interactions in curved spacetime.

Contribution

It introduces a method to incorporate spacetime curvature effects into the Yukawa potential using the Bunch-Parker propagator expansion and applies it to the Reissner-Nordström metric.

Findings

Curvature induces measurable modifications to the Yukawa potential.

Corrections depend on geometric quantities like Ricci scalar and tensor.

Results are relevant for quantum interactions near strong gravitational fields.

Abstract

In this paper, we investigate the influence of the spacetime curvature on the Yukawa potential, focusing on boson-boson interactions derived from the {\Phi^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-Nordstr\"om 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.