Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-11-17
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTex 11 pages, 3 figures
Scientific paper
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.
Eingorn Maxim
Kudinova Alexandra
Zhuk Alexander
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