Emergence of Spacetimes and Noncommutativity

We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only [1]. 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 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.