Singularities and black holes in causal set gravity

The causal set theory is often considered as the simplest approach to quantum gravity, but this simplicity has made it difficult to precisely define black holes in the theory. I first show that the causal set theory is not so simple as we might think, and still admits continuum. I argue that the continuum behaves like a singularity in a certain sense, and propose the internal definition of black holes in the causal set theory based on the continuum.