How Plausible Is the Existence of White Holes?
Although, when talking about white holes and their plausibility, some are quick to harp on the fact that black holes were once thought to be outlandish, and they then apply this example to the white hole case to keep our minds open to the possibility of white holes being existent--and it is usually good to keep our minds open--there is currently not much evidence to support the existence of white holes nor to provide much hope for their actuality. It's definitely not impossible, of course. As for them being the other side of a blackhole, one major issue arises: The singularity that caused the black hole still remains within the black hole, blocking the passage way; so anything that enters the black hole is "stacked" upon that singularity. So unless over some grandiose time scales there occurs some reaction within the black hole which allows for the exit of the matter, possibly some quantum processes, it seems as if black holes don't allow for an exit. However, to keep some balance here, I would say that it's fair to say our understanding of the universe is almost laughably and helplessly jejune in terms of our ability to formulate both the physical dynamics and areas of the universe. So, it's not fair to rule much of any theory out at this point.
However, just to mention here while we are discussing plausibility, there is the presupposition of a multiverse in much of white hole theory. Which of course isn't ridiculous, but it definitely should be mentioned. Also, it appears that as far as we have calculated thus far, white holes appear to violate the second law of thermodynamics. And, their very existence as the time reverse of a black hole in under scrutiny, due to the argument that black holes achieve thermal equilibrium by emitting Hawking radiation and that in a state of thermal equilibrium the time reverse of a black is again a black hole, because the time reverse is invariant.
So for now, the white hole remains a diverse theory and an equation.