Computer simulations of 3-d Lorentzian quantum gravity

We investigate the phase diagram of non-perturbative three-dimensional Lorentzian quantum gravity with the help of Monte Carlo simulations. The system has a first-order phase transition at a critical value k(0)(e) of the bare inverse gravitational coupling constant k(0). For k(0) > k(0)(c) the system reduces to a product of uncorrelated Euclidean 2d gravity models and has no intrinsic interest as a model of 3d gravity. For k(0) < k(0)(e), extended three-dimensional geometries dominate the functional integral despite the fact that we perform a sum over geometries and no particular background is distinguished at the outset. Furthermore, all systems with k(0) < k(0)(c) have the same continuum limit. A different choice of k(0) corresponds merely to a redefinition of the overall length scale.