In a black hole, nothing can come out of the horizon, only in. If you go into the horizon, you are bound to go into the singularity.
In a white hole, nothing can go into the horizon, only out. If you come out of the horizon, you are bound to have come out of the singularity.
The mathematically most symmetrical sort of solution, which we learn about in school but doesn't seem to exist in real life, involves both a black hole *and* a white hole.
There is a lot to say about this....
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