I've been doing some research on white holes, and there has not been enough information to provide the answer. Some websites are saying that they might exist, but it is not yet proven. So, is it true that they exist or not.
Well, currently, we don't have a shred of evidence that they exist.
White holes are hypothetical objects predicted by certain solutions to Einstein's theory of general relativity. To be specific, they come from the maximally extended Schwarzschild solution. We can deal with them a little mathematically, but nobody will really believe in objects like these unless we have experimental evidence for them.
Do we? I quote NASA here
White holes are VERY hypothetical.
There is no observational evidence for white holes.
This supports this position:
Unlike black holes, there is no real astronomical evidence to suggest that white holes actually exist.
Also, the idea is put nicely here:
A white hole is only a concept for higher levels of thinking. No one has every observed one and no one probably ever will.
Why? This gives an interesting answer:
Once even the tiniest speck of dust enters the part of space-time which includes the black hole, the part which includes the white hole disappears. The universe has been around for a long time and so even if it did start with white holes, they would have all disappeared by now. (Emphasis mine)
Essentially, white holes are unstable. Even if a particle did try to enter one from a black hole via an Einstein-Rosen bridge, the bridge would collapse before the particle could cross, and the particle would hit the singularity.
A white hole is simply the time-reversed version of a black hole. For any physical situation, its time-reversal is, formally speaking, possible. It does not mean that it is possible in any physically reasonable sense of the term.
If you release a macroscopic amount of gas in the corner of a large vacuum container, it will spread throughout. There is a physical state that's the exact time-reverse of this, with a gas spread through spontaneously arranging itself in a corner. Yet it does not happen. It's so overwhelmingly unlikely that one can say it is impossible. The reason it doesn't happen is the second law of thermodynamics.
Because of the connection between black hole dynamics and thermodynamics demonstrated by Hawking radiation and similar insights, white holes are are as impossible as cracked eggs spontaneously re-assembling themselves. Or rather, more impossible, because black holes are the most entropic objects in the universe, and so require a much larger violation of the second law.