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Light near a black hole's event horizon


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Working across frames is always difficult/tricky.

 

Consider an observer in freefall crossing the event horizon.

He ( if he had the time ) would measure the event horizon moving radially outward at the speed of light.

Similarly, he would measure the speed of a photon emitted radially outward to be c .

 

This is all perfectly valid so far, it is only when you consider a far-away observer's viewpoint, that, since event horizon and photon are moving outward at the same speed , then they must be stationary with respect o each other.

And this analysis would be wrong because that far-away observer is mixing frames.

 

 

@imatfaal

I thought I had posted #7 as a response to Janus on the other thread about escape velocity at the event horizon ( BH question ). As it makes little sense here, could you please move it back ?

Edited by MigL
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@imatfaal

I thought I had posted #7 as a response to Janus on the other thread about escape velocity at the event horizon ( BH question ). As it makes little sense here, could you please move it back ?

 

Apologies. Done

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Which said action would change the mass-energy of the BH - changing the position of the EH.

 

On another tack:

From a local inertial frame the photon must travel at c, there is no frame of the photon (regardless to your comment above that "every frame of reference is as valid as any other frame" - if you posit an inertial frame in which the speed of light is not locally c then you have contradicted one of the postulates of einstein's relativity and henceforward you cannot rely on the calculations of relativity), and for a distant accelerated frame (ie someone being held in position a distance away) the photon will either be redshifted to obscurity (but still moving) or by your claim will never reach them. So in what frame does it hover

 

Final questions:

What is a stationary photon - ie one not travelling through a medium at the local speed of light, what is its frequency if both c and lambda equal zero(undefined?), what is its energy from planck's equation if frequency is not clear

As a lay person I certainly am not qualified nor knowledgable enough to argue against some of the points you have made, other then again to refer you to Professor Hamilton's link.

What I will do though is E-Mail him expressing your points of view, if that's OK with you.

He, [Professor Hamilton] has been gracious enough to answer in the past.

I also found this...........................

https://physics.stackexchange.com/questions/82984/photon-stuck-on-the-event-horizon-of-a-black-hole

Q:

According to what I've read on special relativity, cc is the speed limit for every object in the universe, and according to Einstein, an object's speed through the three spatial dimensions plus its speed through the fourth temporal dimension always sums to cc.

I once watched a video demonstrating what it would be like to fall into a black hole. At one point the author stated that if a photon was emitted directly away from the singularity and at a distance equal to the Schwarzschild radius, the photon would hover there for eternity.

My question is based on these assumptions so please let me know if either is incorrect.

With its motion through the spatial dimensions halted, will the photon in question not experience time at roughly the same rate we do? Will it decay?

A:

First, a couple things:

  • photons do not "experience" time in general, precisely because they always travel at cc.
  • because of the above point, photons do not decay, either.

To better visualize what's happening, consider that the event horizon is a place where spacetime itself is "falling" into the black hole at the speed of light. So, if you emit a photon precisely as you pass the event horizon, the photon's physical motion through space would be exactly counteracted by the spacetime curvature at the horizon, and it would effectively "hover" at that location.

However, the way that this photon would be observed is very different for different observers:

The in-falling observer, who emits the photon just as she passes the event horizon, will believe that the photon is traveling away from her (at cc, as usual).

However, a distant observer (far from the black hole) will never see the photon at all. Or rather, to the distant observer, the photon will appear to be infinitely redshifted.

An observer who falls into the black hole after the first in-falling observer still has a chance to observe the photon (not redshifted).

But more practically speaking, this kind of "equilibrium" would be highly unstable (the photon would not be able to "hover" for very long). This is because the black hole's Schwarzschild radius is always changing slightly, whether it's due to the black hole absorbing CMB radiation, or emitting Hawking radiation. So, the photon will eventually either escape, or be dragged deeper into the black hole.

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Taking into account the BH consuming more matter and the EH getting bigger, or the possibility of HR evaporating the BH over time, the statement of mine about hovering "forever" early in the thread, does appear to be in error.

I do see the answer as supplied, a valid response with no anomalies, but will still E-Mail Professor Hamilton:

Edited by beecee
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Taking into account the BH consuming more matter and the EH getting bigger, or the possibility of HR evaporating the BH over time, the statement of mine about hovering "forever" early in the thread, does appear to be in error.

 

 

Although, it is worth noting that the Schwarzschild metric is an idealisation based on an eternal, unchanging spherical mass. So, based on that model it could be there forever. But, obviously, the thought experiment is unrealistic for multiple reasons.

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