Newton's Law Modifications due to a Sol Manifold Extra Dimensional Space

TL;DR

This paper investigates how a Sol manifold as an extra dimension modifies Newton's gravitational law, revealing that the size of the extra dimension significantly influences the magnitude of these corrections.

Contribution

It introduces the analysis of gravitational potential corrections due to a Sol manifold extra dimension, comparing them with known torus compactifications.

Findings

For small radii ($R<10^{-6}$), Sol manifold corrections are significantly larger.

Corrections vary with radius, being larger, comparable, or smaller than torus corrections.

The study highlights the impact of manifold geometry on gravitational modifications.

Abstract

The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as $M_A^3$, are studied. The total spacetime is $M^4\times M_A^3$. We compare the range of the corrections to the range of the $T^3$ corrections. It is found that for small values of the radius of the extra dimensions ($R<10^{-6}$) the the Sol manifold corrections are large compared to the 3-torus corrections. Also, Sol manifolds corrections can be larger, comparable or smaller compared to the 3-torus case, for larger $R$.