Gravity and the Structure of Noncommutative Algebras

Abstract

A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time.

17 pages

References in corpus (6)

• Gravity coupled with matter and foundation of non-commutative geometry
• Noncommutative Geometry and Gravity
• Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory
• Can noncommutativity resolve the Big-Bang singularity?
• On Poisson Structure and Curvature
• A Dynamical 2-dimensional Fuzzy Space

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• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Four-dimensional Gravity on a Covariant Noncommutative Space
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• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Noncommutative gravity and the relevance of the $\theta$-constant deformation
• Noncommutative gravity with self-dual variables
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• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Intertwining noncommutativity with gravity and particle physics
• Gravitational collapse of spherically symmetric stars in noncommutative general relativity
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Phase space quantization, noncommutativity and the gravitational field
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• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Noncommutative geometry of phase space
• QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly