Noncommutative gravity: fuzzy sphere and others

Abstract

Gravity on noncommutative analogues of compact spaces can give a finite mode truncation of ordinary commutative gravity. We obtain the actions for gravity on the noncommutative two-sphere and on the noncommutative ${\mathbf{CP}}^2$ in terms of finite dimensional $(N\times N)$-matrices. The commutative large $N$ limit is also discussed.

LaTeX, 13 pages, section on CP^2 added + minor changes

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Cited by in corpus (20)

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• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Noncommutative Self-dual Gravity
• Noncommutative BTZ Black Hole and Discrete Time
• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem
• Non Commutative Bianchi type II Quantum Cosmology
• Chiral spinors and gauge fields in noncommutative curved space-time
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Inherent Holography In Fuzzy Spaces and An N-tropic Approach To The Cosmological Constant Problem
• Spherically symmetric monopoles in noncommutative space
• Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology
• WKB-type Approximation to Noncommutative Quantum Cosmology
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Intertwining noncommutativity with gravity and particle physics
• Infinities as a measure of our ignorance
• A note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects