Why can’t you fall into a white hole? Part III: It takes two to tango.
Continued from Part II.
Last time we saw that if someone decided to plunge into a white hole, there is nothing preventing them from reaching the horizon in the finite time. The question was, what happens next, given that there is no way to cross the white hole horizon inward, just like there is no way to cross the black hole horizon outward? To make progress in answering this question, let’s imagine what someone reaching the horizon would feel. He (to pick a gender pronoun at random) would notice the usual tidal gravity forces stretching him in the direction of the fall and squeezing him in the perpendicular directions.
And by the way, Einstein tells us that the squeezing force per unit distance in the two perpendicular directions together is equal to the stretching force per unit distance in the direction of the fall. (The “per unit distance” qualifier here is essential: tidal forces are always like that: the large the object, the stronger the tidal force.) And the closer you get to the horizon, the stronger these tidal forces get, whether it’s the black hole or the white hole horizon. Oh, and nothing special happens in your vicinity when you cross the horizon, you just keep falling. The horizon is a point of no return, to be sure, but you wouldn’t know it unless you actually tried to return.
So, you reach the white hole horizon, and you keep going, and the tidal forces keep kneading you into mush, eventually ripping you apart… Wait, what? I am describing the act of falling into a black hole, am I not. Well, right you are. So, what is this BS about white holes then? Ah. Remember, falling into the white hole, at least up until the horizon, is just like going away from a black hole, only with the time running backwards. And since there is nothing special about the horizon, you ought to go through it like there is no tomorrow… Which there won’t be, of course. But I digress.
Yes, falling into a white hole feels just like falling into a black hole, only you run a chance of being hit by the random junk coming out of the white hole and die somewhat prematurely, if not very much so. You see where it is going now, do you? Toward the singularity in the future of the infalling observer. Moreover, once you cross the horizon, you cannot get back. So, what I am really describing is that, from the point of view of the guy falling in, he is falling into a black hole. While from the point of view of a guy falling out, he is falling out of a white hole.
Which means that every white hole is also a black hole. Like Yin and Yang, they come in pairs. Let me qualify that. Any potential white hole would have to be paired up with a black hole. But it is not necessarily true that any black hole has to be paired with a white hole. In fact, it is most likely that they are not. Black holes are formed when massive stars collapse, and there is no obvious way to create a white hole in this process. In fact, we don’t know of any way to form a white hole. Maybe some could have formed during the Big Bang, and survived until the present day, who knows. This is a pure speculation. But if some did form and survived, they would most certainly be paired with black holes.
Now to summarize my answer to the title question: you cannot fall into a white hole because what you would really be falling into is a black hole!
But this is only scratching the surface, so to speak, of the tangled black hole/white hole relationship. For example, if something falls into a black part of the pair, and the black hole grows in size and mass, does the mass of the associated white hole change? Or, if you nudge the black hole with something really heavy, do you also move the white hole? if so, how can you, the white hole singularity is in the past, and you cannot change the past, can you? Also, what about the famous Hawking radiation? Does it come out of the white hole horizon? I hope to get to discussing these questions some day.
To learn more: eternal white holes and black holes are described in a semi-accessible way in the book Black Hole Physics: Basic Concepts and New Developments, by Valeri Frolov and Igor Novikov.