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

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.

35 pages, 4 figures. V2: Minor corrections and discussion added, published version

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Cited by in corpus (11)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• 2D fuzzy Anti-de Sitter space from matrix models
• Large Distance Modification of Newtonian Potential and Structure Formation in Universe
• On the 1-loop effective action for the IKKT model and non-commutative branes
• Quantum Gravity from Noncommutative Spacetime
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Brane compactifications and 4-dimensional geometry in the IKKT model
• Gravity and compactified branes in matrix models
• The curvature of branes, currents and gravity in matrix models
• Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions