2006/07/31 by E. Harikumar, Victor O. Rivelles · 6 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Mathematical physics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/23/24/024
published as Class.Quant.Grav.23:7551-7560,2006 · 11 pages, more references added
arxiv created 2006/10/25 · openalex publication_date 2006/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider simple extensions of noncommutativity from flat to curved spacetime. One possibility is to have a generalization of the Moyal product with a covariantly constant noncommutative tensor θ μν . In this case, the spacetime symmetry is restricted to volume-preserving diffeomorphisms which also preserve θ μν . Another possibility is an extension of the Kontsevich product to curved spacetime. In both cases, the noncommutative product is nonassociative. We find the order θ 2 noncommutative correction to the Newtonian potential in the case of a covariantly constant θ μν . It is still of the form 1/ r plus an angle-dependent piece. The coupling to matter gives rise to a propagator which is θ dependent.