Chronos said:
it is generally held that a black hole is the opposite of the big bang.
I don't think this is correct except in the obvious (and very coarse) sense that black holes are formed by collapse whereas the Big Bang involves expansion. (There is also a technical sense in which the singularities in both cases are the "opposite" of each other, but it's very weak--see below.)
The "opposite" of a black hole (in the sense of "time reverse") is a white hole, and the Big Bang is not a white hole, because a white hole has a horizon that separates the hole's singularity from past null infinity. There is no past null infinity in the Big Bang spacetime. Similarly, the opposite (again in the sense of time reverse) of the Big Bang is a Big Crunch, and the Big Crunch is not a black hole, because a black hole has a horizon that separates the hole's singularity from future null infinity, and there is no future null infinity in a Big Crunch spacetime.
It is true, as I mentioned above, that the Big Bang singularity and a black hole singularity are both spacelike singularities; but the similarity ends there. The Big Bang singularity had zero tidal gravity (except for the small "wrinkles" that got magnified by inflation into the small anisotropies in the CMBR that we detect today). A black hole singularity, by contrast, at least for any real black hole (as opposed to an idealized one that is formed by a perfectly spherically symmetric collapse and remains perfectly spherically symmetric for all time), has *lots* of tidal gravity, as you note. So even if we ignore the difference of horizon vs. no horizon that I described above, a black hole and the Big Bang are not "time reverses" of each other, because of the huge difference in tidal gravity. (A "real" Big Crunch, at least as far as I can tell from what I've read, is modeled as having large tidal gravity, so it isn't quite the time reverse of the Big Bang either, and its singularity would be more like a black hole singularity in that respect--though it still differs with regard to the lack of a horizon or a future null infinity.)