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 Gμν = 0 and the Minkowski metric is also found. All solutions we obtained are non-perturbative in the noncommutative parameter θ, therefore they are different from solutions found in other contexts of noncommutative theory of gravity and would have a close relation to quantum gravity.
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