Non-relativistic limit of Randall-Sundrum model: solutions, applications and constraints

TL;DR

This paper derives solutions for gravitational potentials in the Randall-Sundrum model, compares approximate and exact results, and establishes an upper limit for the model's curvature scale parameter based on force correction differences.

Contribution

It provides both approximate and exact solutions for gravitational effects in the Randall-Sundrum model and determines constraints on the model's parameters from these solutions.

Findings

The difference between approximate and exact force corrections increases with the parameter l.

The difference also increases as the distance between spheres decreases.

Upper limit for the curvature scale parameter l is approximately 10 micrometers.

Abstract

In the Randall-Sundrum model with one brane, we found the approximate and exact solutions for gravitational potentials and accelerations of test bodies in these potentials for different geometrical configurations. We applied these formulas for calculation of the gravitational interaction between two spheres and found the approximate and exact expressions for the relative force corrections to the Newton's gravitational force. We demonstrated that the difference between relative force corrections for the approximate and exact cases increases with the parameter $l$ (for the fixed distance $r$ between centers of the spheres). On the other hand, this difference increases with decreasing of the distance between the centers of the spheres (for the fixed curvature scale parameter $l$). We got the upper limit for the curvature scale parameter $l\lesssim 10\, \mu$m. For these values of $l$, the difference between the approximate and exact solutions is negligible.