Noncommutative self-dual gravity

2003/02/23 by H. Garcia-Compean, Hugo García‐Compeán, O. Obregón +4 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Commutative property #Cosmology and Gravitation Theories #Dual (grammatical number) #Einstein #Gravitation #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Philosophy #Physics #Pure mathematics #Torsion (gastropod) #hep-th

paper · pdf · doi:10.1103/physrevd.68.044015

published as Phys.Rev. D68 (2003) 044015 · 15+1 pages, LaTeX, no figures

arxiv created 2003/02/23 · openalex publication_date 2003/08/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use the Seiberg-Witten map. A procedure is outlined that allows one to find the solution of the noncommutative torsion constraint through the vanishing of the commutative one. Finally, the noncommutative corrections to the action are computed up to second order.

Citations

• Quantum gravity: a progress report
• String theory and noncommutative geometry
• Lorentz Invariance and the Gravitational Field
• Construction of non-Abelian gauge theories on noncommutative spaces
• The standard model on non-commutative space-time
• Deforming Einstein's gravity
• Gravitational fields on a noncommutative space
• New Variables for Classical and Quantum Gravity
• Mtheory as a matrix model: A conjecture
• New Hamiltonian formulation of general relativity
• Invariant Theoretical Interpretation of Interaction
• Noncommutative geometry and Matrix theory

Cited by

• Noncommutative gravity with self-dual variables
• Symmetry, gravity and noncommutativity