  We explicitly compute the causal structure of the Schwarzschild black hole
spacetime, by providing an algorithm to decide if any pair of events is
causally related. The primary motivation for this study comes from discrete
quantum gravity, in particular the causal set approach, in which the
fundamental variables can be thought of as the causal ordering of randomly
selected events in spacetime. This work opens the way to simulating
non-conformally flat spacetimes within the causal set approach, which may allow
one to study important questions such as black hole entropy and Hawking
radiation on a full four dimensional causal set black hole.
