Schwarzschild vs Gullstrand–Painleve and event horizons

[Pittman]

Now my question is about these two systems is how they handle time at the event horizon. Now if I understand correctly the Schwarzschild coordinates states that as you reach the event horizon of a black hole that time reaches infinity thus time has stopped using this system. Now with the Gullstrand–Painleve coordinates since they will go past the event horizon that time doesn’t reach infinity thus time doesn’t stop until it reaches the singularity of the black hole. With both of these systems it would be the observation of the distant observer as watching someone fall to a black hole, do I understand this correctly?

 

[Bill_K]

You might try taking a look at Eddington coordinates, they're better adapted to talking about these things than Painleve coordinates, in my opinion. Whichever you use, they both come in two varieties: advanced and retarded, one being the time reversal of the other. One is useful for inward-going radial geodesics, the other for outward-going.

It's not correct to say that "time stops". Time never stops, and I'm sure you realize that the falling observer senses nothing strange locally when he crosses the event horizon at r=2m. It's the global coordinate system that may go bad, and as you say the Schwarzschild time runs to infinity there. Eddington coordinates (or Painleve coordinates) provide a cure (a better time variable) for the inward-going geodesics.

None of this affects what an observer at spatial infinity would see.

 

[tom.stoer]

The Schwarzschild coordinates encode what a far distant observer would see, what he would call "time". But physically one must calculate the proper time of the observer in free fall eventually crossing the event horizon and hitting the singularity. This can be done in nearly all coordinates (some are better under control) and you will always get the same result fot the elapsed proper time for the observer reaching the singularity.