Scalar-Graviton Scattering in Noncommutative Space and Deformed Newton Gravity

TL;DR

This paper extends the analysis of noncommutative space effects on Newtonian gravity by deriving a relativistic scalar-graviton scattering amplitude, revealing a momentum-dependent potential.

Contribution

It generalizes previous noncommutative gravity models to the relativistic regime through explicit scattering amplitude calculations.

Findings

Newton potential becomes momentum-dependent in noncommutative space

Relativistic scattering amplitude confirms deformation of gravitational potential

Isotropy of Newton potential is broken in noncommutative geometry

Abstract

The isotropy of Newton potential in noncommutative space disappears as it deforms to a momentum dependent one. We generalize the earlier derivation of such a deformed potential to the relativistic regime by calculating the 2 scalar-1 graviton scattering amplitude by taking into account the noncommutativity of space.