2003/03/13 by Paolo Valtancoli, P. VALTANCOLI
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Covariant transformation #Gauge group #Gauge theory #Gravitation #Instanton #Lorentz group #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Spin connection #hep-th
paper · pdf · doi:10.1142/s0217751x04017586
published as Int.J.Mod.Phys. A19 (2004) 227-248 · 28 pages, LaTeX, no figures
arxiv created 2003/03/13 · openalex publication_date 2004/01/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We introduce a matrix model for noncommutative gravity, based on the gauge group U (2)⊗ U (2). The vierbein is encoded in a matrix Y μ , having values in the coset space U (4)/( U (2)⊗ U (2)), while the spin connection is encoded in a matrix X μ , having values in U (2)⊗ U (2). We show how to recover the Einstein equations from the θ→0 limit of the matrix model equations of motion. We stress the necessity of a metric tensor, which is a covariant representation of the gauge group in order to set up a consistent second order formalism. We finally define noncommutative gravitational instantons as generated by U (2)⊗ U (2) valued quasi-unitary operators acting on the background of the matrix model. Some of these solutions have naturally self-dual or anti-self-dual spin connections.