Black Holes: Infalling Observers and BH Evaporation

[PAllen]

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 Schwarzschild 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.

 

[Naty1]

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.

 

[Chronos]

For a video see http://jila.colorado.edu/~ajsh/insidebh/schw.html.

 

[SHISHKABOB]

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

 

[Chronos]

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
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."

 

[PAllen]

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
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.

 

[Chronos]

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]

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).