Noncommutative Solitons of Gravity

Abstract

We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only. We found various kinds of nontrivial solutions, by applying a similar technique which was used to seek noncommutative solitons in noncommutative scalar field theories. Some of those solutions correspond to bubbles of spacetimes, or represent dimensional reduction. The solution which interpolates $G_{\mu \nu }=0$ and Minkowski metric is also found. All solutions we obtained are non-perturbative in the noncommutative parameter $\theta$, therefore they are different from solutions found in other contexts of noncommutative theory of gravity and would have a close relation to quantum gravity.

29 pages, 5 figures. v2: minor corrections done in Section 3.1 and Appendix, references added. v3, v4: typos corrected

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Cited by in corpus (7)

• Field Theory on Curved Noncommutative Spacetimes
• Tensor calculus on noncommutative spaces
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• Regular Black Holes and Noncommutative Geometry Inspired Fuzzy Sources
• Angles in Fuzzy Disc and Angular Noncommutative Solitons
• Spacetime Noncommutativity in Models with Warped Extradimensions