Corrections to Gravity due to a Sol Manifold Extra Dimensional Space

TL;DR

This paper investigates how a Sol manifold as an extra dimension affects gravitational potential corrections, comparing its range to that of a toroidal extra dimension, within a spacetime model of four dimensions plus a three-dimensional compact manifold.

Contribution

It introduces the analysis of gravitational corrections from a Sol manifold as an extra dimension, expanding beyond traditional toroidal models.

Findings

Sol corrections have a specific range that differs from T^3 corrections.

The range of gravitational corrections depends on the geometry of the extra dimension.

Comparison shows distinct features between Sol and T^3 compactifications.

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 of the form $M^4\times M_A^3$. The range of the Sol corrections is investigated and compared to the range of the $T^3$ corrections.