Computer simulations of 3d 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 kc 0 of the bare inverse gravitational coupling constant k0. For k0 > kc0 the system reduces to a product of uncorrelated Euclidean 2d gravity models and has no intrinsic interest as a model of 3d gravity. For k0 > kc0, 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 k0 > kc0 have the same continuum limit. A different choice of k0 corresponds merely to a redefinition of the overall length scale.