In "The Hidden Reality", Brian Greene mentions almost off-hand that inside the event horizon of a black hole, space and time are reversed. But no details are given. What, precisely, does this mean? Does it mean that in one's equations, if one is using a (-,-,-,+) signature, then everything switches to a (+,+,+,-) signature? Does it mean that time splits into three dimensions and space into one?? Does it mean that one can see both past and future? That space flows like time did? Many of these possibilities would give lie to the idea in general relativity that an observer traveling towards the singularity of a black hole in free fall would not notice any difference when entering the event horizon (putting aside for the moment the enigma of the possible firewall). I would be grateful to anyone who clears up this statement with some details.