Newton's law in an effective non commutative space-time

TL;DR

This paper calculates the Newtonian potential exactly within a non-commutative space-time framework, analyzing its behavior at different scales when the source distribution's dispersion matches the non-commutative parameter.

Contribution

It provides an exact computation of the Newtonian potential in a fundamentally non-commutative space-time, exploring its properties at various distance scales.

Findings

Potential behavior differs at large and small distances

Exact solutions are obtained for specific source dispersions

Insights into non-commutative effects on classical gravity

Abstract

The Newtonian Potential is computed exactly in a theory that is fundamentally Non Commutative in the space-time coordinates. When the dispersion for the distribution of the source is minimal (i.e. it is equal to the non commutative parameter $\theta$), the behavior for large and small distances is analyzed.