Ask a Physicist
Do white holes exist? If so, how are they formed? Does time exist in white
holes, since they are inverse black holes?
A white hole is indeed the inverse of a black hole, but we don't expect to find one in real life.
Within a year of Einstein developing his general theory of relativity - and saying the equations were too hard to be solved - Karl Schwarzschild found the first solution describing what we now call a black hole. This was the simplest version of a black hole: very symmetric, sitting in isolation for all eternity, no matter falling in, not rotating or changing with time. It became apparent that it had a surface (which got named an event horizon) which you could get into but not out of. Light couldn't get out either, which is why the whole thing eventually got named a black hole.
Later, when people developed more sophisticated mathematical tools to look at such solutions, they realized that wasn't the whole story. The structure of space and time in this simple case had to have what is called time reversal symmetry, which means if you let time run backwards everything should look the same. Therefore if there is a horizon extending into the future which light can enter but not leave, there has to be another horizon extending into the past which light can leave but not enter. That would look like the inverse of a black hole, so they called it a white hole although it's really the extension of the black hole into the past. (And it gets even weirder: There is what looks like another universe inside the horizon, although the meaning of "inside" becomes distorted.) Time would exist inside a white hole, although since you couldn't get in you'd have to be born in there to measure it.
But in real life we don't expect to see white holes, because real black holes are more complicated than this simple solution to the equations of general relativity. They didn't exist infinitely far back in the past, but rather formed some finite time ago by collapsing stars. This ruins the time reversal symmetry, so if you look at past history you don't get the white hole part of the solution but rather a black hole forming towards the end of the stellar collapse.