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

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 $R$.