What is the probability that the other end (opposite)of a black hole is the culmination of a new big ooze (Big Bang)where the captivated matter is compressed and distributed into the universe? It would already have rotation, with energy, matter and gravity compressed; as it emerged and decompressed, would resemble a cloud nebula ready to form into another galaxy and the cycle would begin again anew. In this manner, matter, energy and gravity would be retained even reformed as it exploded from the discharge end of the black hole. After many eons it would resemble a new and different beginning of the universe. In this proposal, there would be no beginning and no end to time and space. Just a continual cycling of matter, energy and gravity and an confirmation to the doughnut theory of the form of the universe..06/29/09
Your take is actually pretty similar to an early version of "white hole" speculation, made famous in the 70s. The notion was that matter-energy sucked into a black hole's event horizon came out in a white hole at some other region of space -time.\
Unfortunately, there is nothing at all to support it, and - with the exception of Hawking's quantum scale ("mini" or "micro") black holes- which can leak radiation, nothing escapes them....ever. So there is no possibility of anything substantial being captured and subsequently "reformed" or escaping. And certainly not enough to provide the basis for a new cosmic origin!
Below is a link to a further answer I gave some time ago (in the astrophysics forum) concerning white holes, and why these entities aren't feasible:
A further note: a universe having "no end to time or space" wouldn't have to issue from a white-hole type scenario such as you portray. All that would be needed is a sufficient mass-density of the cosmos to cause it to re-collapse. Then there would be never-ending "cycles" of: Big Bang -> expansion-> recollapse-> Big Bang-> expansion-> recollapse-> etc. etc.
Alas, the data from numerous sources (e.g. type II supernovae) discloses there isn't enough mass-density to permit this. So the cosmos is a "one life" entity which will go on expanding until its eventual heat death. (No more radiant energy emitted from any sources or any energy conversions at all)