# 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.

## Key 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.