This question is regarding classical blackholes. So inside the event horizon, spacetime behaves strangely. Space is now one dimensional and only in the forward direction(that is, into the singularity) and time of events is preceived as forward and backwards since light from a source comes from both the future and the past. Basically, the behavior of time and space got switched. My question is, 1) why is there an inversion like this? 2) since spacetime behaves so differently inside the event horizon, is this region of spacetime a topologically distinct space, connected merely by the event horizon?