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

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.

LaTex 11 pages, 3 figures

References in corpus (6)

• Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
• A Measurement of Newton's Gravitational Constant
• Constraints on Braneworld Gravity Models from a Kinematic Limit on the Age of the Black Hole XTE J1118+480
• Constraining the braneworld with gravitational wave observations
• Shrinking the Braneworld: Black Hole in a Globular Cluster
• Proposal for an experiment to search for Randall-Sundrum type corrections to Newton's law of gravitation

Cited by in corpus (2)

• Gravitational potential of a point mass in a brane world
• Localization and mass spectra of various matter fields on Weyl thin brane