Application of the proximity force approximation to gravitational and Yukawa-type forces

TL;DR

This paper demonstrates that the proximity force approximation is valid for gravitational and Yukawa-type forces in sphere-plate configurations, supporting previous constraints on non-Newtonian gravity parameters.

Contribution

It extends the application of the proximity force approximation to gravitational and Yukawa interactions, clarifying its validity and correcting recent misconceptions.

Findings

Proximity force approximation is valid for gravitational forces in sphere-plate setups.

The approximation is also valid for Yukawa-type interactions with a simple mapping.

Results support previous constraints on non-Newtonian gravity parameters.

Abstract

We apply the proximity force approximation, which is widely used for the calculation of the Casimir force between bodies with nonplanar boundary surfaces, to gravitational and Yukawa-type interactions. It is shown that for the gravitational force in a sphere-plate configuration the general formulation of the proximity force approximation is well applicable. For a Yukawa-type interaction we demonstrate the validity of both the general formulation of the proximity force approximation, and a simple mapping between the sphere-plate and plate-plate configurations. The claims to the contrary in some recent literature are thus incorrect. Our results justify the constraints on the parameters of non-Newtonian gravity previously obtained from the indirect dynamic measurements of the Casimir pressure.