I definitely get your point. One difference between theoretical physics and just math is we have since we use math as just a tool to describe the world, we still have to input physical assumptions to make any sense of what we see. There are many instances of things being mathematically "OK" but we don't think physically exist. See "White Hole" for instance.
I will try to give a better explanation later today! Funny enough, I am off for the section for the QFT2 that Daniel teaches right now, hah. I can also ask him personally questions later in the week.
Black holes are hard to notice, except by side effects, but we know great many of them, end even portrayed one.
White holes would be relatively hard to miss, because they must be shining very brightly. One of the current theories suggests that the big bang (or "a big bang") was a white hole: every black hole is a white hole producing a big bang a parallel universe. We've already had ours, and are lucky enough to still register its echo as the CMB.
I will try to give a better explanation later today! Funny enough, I am off for the section for the QFT2 that Daniel teaches right now, hah. I can also ask him personally questions later in the week.