On the Newtonian limit of emergent NC gravity and long-distance corrections

TL;DR

This paper demonstrates how Newtonian gravity naturally emerges from non-commutative spacetime branes in Yang-Mills matrix models, revealing long-distance modifications and potential explanations for galactic rotation curves.

Contribution

It shows the emergence of Newtonian gravity and long-distance corrections from non-commutative spacetime branes within the IKKT matrix model framework.

Findings

Large matter clusters create harmonic deformations that screen gravity at large scales.

Local matter distributions reproduce Newtonian gravity through brane deformations.

Galactic orbital velocities are enhanced at large distances before decreasing in a Milne-like cosmology.

Abstract

We show how Newtonian gravity emerges on 4-dimensional non-commutative spacetime branes in Yang-Mills matrix models. Large matter clusters such as galaxies are embedded in large-scale harmonic deformations of the space-time brane, which screen gravity for long distances. On shorter scales, the local matter distribution reproduces Newtonian gravity via local deformations of the brane and its metric. The harmonic ``gravity bag'' acts as a halo with effective positive energy density. This leads in particular to a significant enhancement of the orbital velocities around galaxies at large distances compared with the Newtonian case, before dropping to zero as the geometry merges with a Milne-like cosmology. Besides these ``harmonic'' solutions, there is another class of solutions which is more similar to Einstein gravity. Thus the IKKT model provides an accessible candidate for a quantum theory of gravity.