Black Holes: Infalling Observers and BH Evaporation

[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).