Discrete Black Holes

The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are several discrete models of spacetime like that, some of which have been used to build a (simplified) representation of a black hole. We will shortly revisit these discrete black hole models. Then we limit ourselves to one particular case and show how it can be inhabited by quantum matter fields. It is suggested that the field dynamics should be described by the framework of discrete canonical evolution, and we point out some of the most significant implications of this approach.