> space and time swapping roles once you cross the event horizon This is a common misunderstanding. Space and time don't swap roles. It's just that there's one

> space and time swapping roles once you cross the event horizon This is a common misunderstanding. Space and time don't swap roles. It's just that there's one rather popular coordinate system (Schwarzschild coordinates) whose coordinates t, x outside the horizon correspond to temporal (timelike) and spatial (spacelike) directions, respectively, and inside they correspond to spacelike and timelike directions. What we mean by "timelike" and "spacelike", however, does not change.