In fact, it's the black hole's mirror twin: the white hole. Some even think that these could be the origin of our universe.
We've talked quite a bit about the bizarre behavior of space, and especially time, at and below the event horizon of a black hole.
In a Penrose diagram, the x and y axes are redefined from space and time to merge space and time into new coordinates.
The eternal black hole of the past technically is a white hole.