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

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.