# Black Holes: Infalling Observers and BH Evaporation

Here is another perspective...but I don't like the word 'illusion' as it implies to me something faulty with that distant perspective when it is as valid as any other.

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...
and a related description [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.
Here is another perspective [source unknown] :

..... 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 can't find it, but "As the free-falling observer passes across the event horizon.." Leonard Susskind has explained the 'information' of the infalling object/observer gets 'smeared' across the horizon...so I continue to wonder if one could assume an image of the object remains on the horizon for that distant observer...while the actual infalling object/ observer continues inward, uninterrupted, in his own proper time.

Ah well, time to go and walk my Yorkies!!

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Staff Emeritus
Science Advisor
Interesting. Thanks all!

Here is another perspective...but I don't like the word 'illusion' as it implies to me something faulty with that distant perspective when it is as valid as any other.
Yes. That bothers me too.

Maybe "perspective" or "vantage point" would be better term,

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.
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.

edit: nope, its pervect:
"There's no such thing as a stationary clock at the event horizon..... any clock crossing the event horizon must be moving at the speed of light - or rather, since the event horizon can be thought of as trapped light, any physical infalling clock, which is stationary in its own frame, will see the event horizon approaching it at the speed of light."

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.

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PAllen
Science Advisor
2019 Award
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.
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.

The infaller continues to receive light from distant sources, with no difficulty, until catastrophe at the singularity.

Hey PAllen....

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.
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.
PAllen
Well, I disputed this statement of Chronos, and stand by my disputation.
Disputation!!! Cool [LOL]

Actually we agree. I was NOT trying to sneak in a 'last word' contrary view in the vain hope you would not catch me!!!

It took me a few moments to see my error: I should have quoted simply this from Chronos:

This is because the infaller approaches the speed of light as the event horizon is approached....
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....

Anyway, your posted point that light from the distant cosmos is NOT radically redshifted I have read multiple times and even posted quotes supporting that view elsewhere from Kip Thorne and maybe Brian Greene. So you are in good company!! Cheers.

that's kind of scary, the plain one I mean

Chronos
Science Advisor
Gold Member
This is a complex issue. I found 2 papers dealing with the subject
http://th-www.if.uj.edu.pl/acta/vol39/pdf/v39p1357.pdf [Broken]
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"
http://www-e.unimagdeburg.de/mertens/teaching/seminar/themen/touching_ghosts.pdf
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."

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PAllen
Science Advisor
2019 Award
This is a complex issue. I found 2 papers dealing with the subject
http://th-www.if.uj.edu.pl/acta/vol39/pdf/v39p1357.pdf [Broken]
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"
http://www-e.unimagdeburg.de/mertens/teaching/seminar/themen/touching_ghosts.pdf
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."
Looking at the first paper, I view it as agreeing with everything I said:

- in SC geometry you can factor gravitational and kinematic red shift
- for the infaller receiving signals from a distant observer, the two effects work against each other: gravitational blue shift reducing the kinematic red shift
- the balance of cancellation depends on where free fall starts from; starting free fall from closer to the horizon produces less red shift as the free faller crosses the horizon
- there is an extreme asymmetry in that the two effect add to each (rather than work against each other) other for signals from the infaller to the distant observer, leading to infinite redshift as the free faller approaches the horizon.

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Chronos
Science Advisor
Gold Member
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?

PAllen
Science Advisor
2019 Award
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?
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).