and a related description [source unknown]From Kip Thorne in BLACK HOLES AND TIME WARPS
when the star forms a black hole:
Finkelstein's reference frame was large enough to describe the star's implosion ...simultaneously from the viewpoint of far away static observers and from the viewpoint of observers who ride inward with the imploding star. The resulting description reconciled...the freezing of the implosion as observed from far away with (in contrast to) the continued implosion as observed from the stars surface....an imploding star really does shrink through the critical circumference without hesitation....That it appears to freeze as seen from far away is an illusion....General relativity insists that the star's matter will be crunched out of existence in the singularity at the center of the black...
Here is another perspective [source unknown] :One often sees people interested in the question "where is the infalling probe "now"". For instance, they want to know if the probe has crossed the horizon "now" yet, or not. The best answer to this question is the same as it was in special relativity - there is no universal notion of "now" - the question is ambiguous. It may be slightly annoying to attempt to think of everything in terms of the raw data that one will actually receive (such as curves of redshift vs time), but this is really the safest course. Thinking of things in terms of "where the probe is now" will inevitably lead to confusion, because there is no universal definition of what "now" means, different observers will regard different points as being simultaneous even in SR, and this does not change in GR.
..... the Schwarzschild metric has a coordinate singularity at the event horizon, where the coordinate time becomes infinite. Recall that the coordinate time is approximately equal to the far away observer's proper time. However, a calculation using transformed coordinates shows that the infalling observer falls right through the event horizon in a finite amount of time (the infalling observer's proper time). How can we interpret solutions in which the proper time of one observer approaches infinity yet the proper time of another observer is finite?
The best physical interpretation is that, although we can never actually see someone fall through the event horizon (due to the infinite redshift), he really does. As the free-falling observer passes across the event horizon, any inward directed photons emitted by him continue inward toward the center of the black hole. Any outward directed photons emitted by him at the instant he passes across the event horizon are forever frozen there. So, the outside observer cannot detect any of these photons, whether directed inward or outward.
There's no coordinate-independent way to define the time dilation at various distances from the horizon—a clock is ticking relative to coordinate time, so even if that rate approaches zero in Schwarzschild coordinates which are the most common ones to use for a nonrotating black hole, in a different coordinate system like Kruskal-Szekeres coordinates it wouldn't approach zero at the horizon,
I believe Chronos explains this by noting that the horizon can be viewed as a light hypersurface....which is moving at lightspeed...I don't fully understand that perspective that but he's seem right about everything else.This is because the infaller approaches the speed of light as the event horizon is approached making it increasingly difficult for external photons to 'catch up' with the infaller.
Well, I disputed this statement of Chronos, and stand by my disputation. From the point of view of the free faller, light from distant sources is not highly redshifted, and distant clocks do not appear to run very slow. On the other hand, the distant observer does see light from the infaller extremely redshifted and their clocks run slow then stop. I provided two different explanations of these facts.I believe Chronos explains this by noting that the horizon can be viewed as a light hypersurface....which is moving at lightspeed...I don't fully understand that perspective that but he's seem right about everything else.
One thing I do understand: Approaching a big BH from the exterior is no different than approaching a big dense planet...except, I guess, the BH is, well, black....the gravity itself [gravitational potential] is strong up close, but the gravitational potential gradient [the curvature of tidal force spaghettification] is nothing unusual. In other words, the gravitational gradient becomes extreme at the singularity not at the horizon; apparently the only 'unusual' thing at the horizon is a Schwarszchild coordinate ['fictitous'] singularity in time....so things appear to slow down from a stationary distant frame, but locally to a free falling observer things all seem 'normal' and no horizon can even be detected by such an soberver.
PAllenThis is because the infaller approaches the speed of light as the event horizon is approached making it increasingly difficult for external photons to 'catch up' with the infaller.
I believe Chronos explains this by noting that the horizon can be viewed as a light hypersurface....which is moving at lightspeed...I don't fully understand that perspective that but he's seem right about everything else.
Disputation!!! Cool [LOL]Well, I disputed this statement of Chronos, and stand by my disputation.
because I thought he might be adopting a perspective relative to the event horizon....I was only wondering about looking inward toward the black hole...... I have never quite understood that perspective. I figure I am missing something if both he and pervect have adopted that 'frame' [bad word I know] for some reason I still do not get....This is because the infaller approaches the speed of light as the event horizon is approached....
Looking at the first paper, I view it as agreeing with everything I said:This is a complex issue. I found 2 papers dealing with the subject
DECOUPLING OF KINEMATICAL TIME DILATION AND GRAVITATIONAL TIME DILATION IN PARTICULAR GEOMETRIES
" ... One can find that in the case of a radial fall in Schwarzschild geometry, light signal sent by an IO [remote observer] is received by an IFO [in-falling observer] as a red-shifted one"
Touching ghosts: observing free fall from an infalling frame of reference into a Schwarzschild black hole
"... Less well known is the frequency ratio relation accompanying mutual signal exchange between Alice and her ‘mother station’, MS, located at r0. Namely, one finds that the frequency ratio is redshifted in both cases."
Yes, I agree. The amount of such redshift at time of horizon cross can be reduced, and I think even reversed, by starting free fall from sufficiently close to the horizon (with mothership far away and stationary - well defined in SC geometry).I agree gravitational redshift is a factor for an observer in free fall. Thanks for pointing that out. Apparently, however, it is not enough to entirely offset the kinematical component. Do you agree both papers assert signals from the 'mothership' to a radially infalling observer are redshifted by a non-trivial amount?