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I know a little bit about white holes. I know that they are formed inside eternal black holes. I just need to get my facts clear. As far as I can understand, when an object goes near the event horizon of a black hole, it experiences extreme time dilation (due to the extreme gravity there), so, to an observer beyond a minimum distance, the object should appear to be moving slower and slower as it approaches the event. To account for the decrease in speed and hence, acceleration, the observer imagines another body (white hole) that is applying the force on the object. If this is true, then white holes are nothing more than something like pseudo force, that is simply used to make the answer match with the calculated results. If so, what is its real significance? I am not sure if my thinking is correct, please feel free to correct me.

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White holes were NOT introduced to explain the decrease in the shapiro-delayed velocity due to the gravitational time dilation, for that you only need to know that the local time runs slower by a factor of

$\rm d\tau/dt=\sqrt{1-v_{esc}^2/c^2}$

and the radial gravitational length contraction $\rm dr/dR$, which has the same factor. Since the observed radial velocity is $\rm dr/dt$ this decreases by a factor of

$\rm v^{\parallel}_{local}/v^{\parallel}_{observed}=1-v_{esc}^2/c^2$

when approaching $\rm r=r_H$, with $\rm r_H$ being the radial coordinate of the event horizon, in the Schwarzschild case

$\rm r_H=2GM/c^2$ and $\rm v_{esc}=c \ \sqrt{r_H/r}$

The local radial velocity on the other hand is not $\rm dr/dt$ but $\rm dR/d\tau$, so this does NOT decrease but increase when approaching the horizon.

White holes have nothing to do with this, whoever told you that told you something wrong.

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The basic reason why white holes show up in relativity theory is because Einstein's equations are time-reversible, but when something falls into a black hole, it never re-emerges. You solve this paradox by realizaing that the time-reversed path of something falling into a black hole in the future is that object emerging from a white hole in the past. It is expected that our exact universe had initial conditions that preclude there having been white holes, and that if you go into the distant past, you will eventually reach a matter distribution, and eventually, the big bang.

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