« on: 26/03/2009 12:37:35 »
I'm not familiar with Gullstrand-Painlev coordinate systems - interesting name though - but as there's an absolute difference in the elapsed durations if the clocks are reconciled when the traveling clock returns to the same reference-frame as the observer, I can't see it making much difference because whatever coordinate system they're in, it will apply to both but won't cancel the difference.
I might have misunderstood you there though.
I see it as there will be a time dilation too LeeE, between the observer outside the BH and the observer at the Eventhorizon (traveling clock) but that time change depends on them being in different 'spheres' of place and time. And as my view says that 'time' as observed by you, wherever you might be, only can come to a standstill as seen from your own perspective (traveling clock) at 'c' then time can't stop for you, as long as you are made of matter.
Another thing is that, no matter how near 'c' you might put yourself traveling, I still expect you to observe your own frame of reference and time coordinates to behave as usual (biological clock), even though red and blueshift and spatial 'distortions' will appear as observed when comparing 'frames of reference'. And that experience will hold true for a black hole too, as I see it.
Although when falling into a black hole the gravitational forces will be accompanied by time-dilation and as you there will be in a accelerating system as I understands it your 'biological clock' will be dispersed in a undecidable number of 'time zones' So this depends on how you define your system I think. But given a 'clock' small enough one might expect it to be able to 'transit' in between those different 'timezones'. On the other hand, if time is a flow then perhaps gravity could be seen so too? And in that case there will be an 'infinity' of 'timezones' to fall through and there will be no possibility to create a smallest 'clock' transitioning those 'timezones' created by the black holes gravitywell.
Thinking of why some expect to see that redshifted image of the 'traveling clock' frozen at the Eventhorizon I think they are seeing it as that redshifted light having to traverse out of a gravitywell it also will have to take it a immense time walking back up that 'slope' As you could see a redshift depicting a stretched wave in time, looking at it this way its not the wave that becomes longer, its rather the timedimension that 'stretches out' taking the wave with it. But that information received by the redshift is not the object so you could, as I see it, disregard it as a 'optical illusion' caused by time expanding.
This one describes both 'metrics' http://www.mysearch.org.uk/pdfFiles/6Science/Schwarzschild.PDF , one might possibly say with a slight bias towards the Schwarzschild metric.