Argh I just accidentally deleted my response and I was almsot done too!
Ok, starting over...
I've never heard of a "time reverse opposite." If such a term were to accurately describe a white hole, then wouldn't black holes created far in the future have white hole equivalents that are detectable now?
A black hole doesn't "eat" energy, that implies the often-misused vacuum cleaner idea. Matter and energy are not "sucked in" or "eaten" by a black hole; matter and energy fall into a black hole, as a meteor falls to earth, or a guy falls off a building (because of earth's gravity).
One more thing, which I think debunks all theories of white holes in relation to black holes -
As a black hole accumulates mass, its Schwarzchild Radius (the distance the event horizon is from the center of mass of the black hole) increases. A black hole accumulats mass because matter and energy fall into the black hole (due to its gravity). I do not know exactly how the energy is converted into mass, nut energy and mass are interchangeable - the equation E=mc^2 comes to mind, though. We know the matter and energy are not going anywhere (i.e. through some tunnel in space-time to a white hole) because the Scwarzchild radius does not decrease. This means that the mass is not decreasing.
If a black hole "fed" a white hole with matter/energy, then the black hole would not last very long. Remember a black hole is only a black hole because the star could not support its own weight. I'm not saying that it would turn back into a star, but it would not be a black hole much longer.
If I am not making any sense in one place or another, I apologize, my mind has been wandering these past few days...