Diffeomorphism covariant star products and noncommutative gravity
arXiv:0904.3079 · doi:10.1088/0264-9381/26/14/145010
Abstract
The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of all two-dimensional dilaton gravity models thus overcoming some difficulties of earlier approaches. One of such models appears to be integrable. We find all classical solutions of this model and discuss their properties.
8 pages, v2, v3: references and comments added
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Cited by in corpus (15)
- Gauge Theories on Deformed Spaces
- Field Theory on Curved Noncommutative Spacetimes
- Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
- Noncommutative gravity with self-dual variables
- Noncommutative Particles in Curved Spaces
- Tensor calculus on noncommutative spaces
- Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
- Non-commutative Kerr black hole
- Noncommutative Solitons of Gravity
- Covariant star product on symplectic and Poisson spacetime manifolds
- Contravariant geometry and emergent gravity from noncommutative gauge theories
- Field Theory with Coordinate Dependent Noncommutativity
- Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
- Symplectic connections and Fedosov's quantization on supermanifolds
- Covariant Star Product on Semi-Conformally Flat Noncommutative Calabi-Yau Manifolds and Noncommutative Topological Index Theorem