Computer simulations of 3-d Lorentzian quantum gravity

Abstract

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 c 0 of the bare inverse gravitational coupling constant k 0. For k 0 > k c 0 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 c 0, 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 c 0 have the same continuum limit. A different choice of k 0 corresponds merely to a redefinition of the overall length scale.