Speed of light within a black hole

[nettleton]

I assume that, via scattering processes, the speed of light slows from that in a vacuum close to the centre of a black hole to zero at the event horizon. How is the gradient in its speed defined throughout this volume? Is an analogy with a sound wave reaching an interface appropriate?

 

[phinds]

I assume that, via scattering processes, the speed of light slows from that in a vacuum close to the centre of a black hole to zero at the event horizon. How is the gradient in its speed defined throughout this volume? Is an analogy with a sound wave reaching an interface appropriate?

The speed of light in a vacuum is c. The Event Horizon is a non-physical (i.e. mathematical only) surface that has no effect on the speed of light. I think you are being confused by the fact that a distant observer, when receiving light from near the EH sees it arriving at c but significantly redshifted.

 

[newjerseyrunner]

Or you could be confused by someone telling you that in general relativity TIME slows down to a stop near black holes. That's greatly simplified and only (heuristically) true from the point of view from outside the event horizon. For objects passing through it, time passes normally.

 

[nettleton]

Am I to assume that light is not generated within the black hole but only close to the E.H.? Again, do I consider that, as time slows to zero close to a B.H., c tends to infinity?

 

[phinds]

Am I to assume that light is not generated within the black hole but only close to the E.H.?

No. If you turn on a flashlight inside the EH, it emits photons at c

Again, do I consider that, as time slows to zero close to a B.H., c tends to infinity?

No, light escaping from the environs of an EH arrives at c, just red shifted. Read post #2.

And AGAIN, time does NOT slow down near an EH, it just seems that way to a distant observer.

 

[Nugatory]

Am I to assume that light is not generated within the black hole but only close to the E.H.? Again, do I consider that, as time slows to zero close to a B.H., c tends to infinity?

If you were to take a physics lab with some physicists in it, enclose it in a windowless box, and drop it into a black hole, the physicists inside would not detect anything interesting or different as they approached and fell through the event horizon. If they were doing experiments to measure the speed of light, it would be $c$ far from the event horizon, near the event horizon, at the event horizon, inside the event horizon, and up until they and their lab are destroyed near the central singularity.

Two notes:
1) This is the prediction given by general relativity, which has been extensively tested outside event horizons. There's no way of testing the theory at or inside an event horizon, but also no reason to think that the theory might break down there.
2) This prediction assumes that the black hole is large enough that tidal effects across the box containing the lab are negligible. If this assumption is not valid, the lab will be destroyed by these effects before it ever gets to the event horizon.

 

[rootone]

If you were to take a physics lab with some physicists in it, enclose it in a windowless box, and drop it into a black hole ...

Will put that on my list of things to do.

The speed of light in space is the same everywhere.
Space can be curved though, the Earth is a curved surface in space.
In a black hole the curvature becomes infinite.
Yes that is a problem.

 

[BenAS]

If you were to take a physics lab with some physicists in it, enclose it in a windowless box, and drop it into a black hole, the physicists inside would not detect anything interesting or different as they approached and fell through the event horizon. If they were doing experiments to measure the speed of light, it would be $c$ far from the event horizon, near the event horizon, at the event horizon, inside the event horizon, and up until they and their lab are destroyed near the central singularity.

Two notes:
1) This is the prediction given by general relativity, which has been extensively tested outside event horizons. There's no way of testing the theory at or inside an event horizon, but also no reason to think that the theory might break down there.
2) This prediction assumes that the black hole is large enough that tidal effects across the box containing the lab are negligible. If this assumption is not valid, the lab will be destroyed by these effects before it ever gets to the event horizon.

What if they put a clock at the ceiling, and one on the floor, and watched them both from the middle of the room? Would the difference in gravitational time dilation between the clocks be different from what it would be if the lab was on the surface of the earth? (If in principle they could measure accurately enough)

 

[Nugatory]

What if they put a clock at the ceiling, and one on the floor, and watched them both from the middle of the room? Would the difference in gravitational time dilation between the clocks be different from what it would be if the lab was on the surface of the earth?

Strictly speaking, it's not a "difference in gravitational time dilation" that they're measuring, it's the difference between the rates of the two clocks, which is the time dilation. But with that said...

Whether it's greater or less than the effect at the surface of the Earth (which has been measured - google for "Pound-Rebka") will depend on the size of the black hole. The larger the black hole, the smaller the tidal effects across a given distance; but it would take a very large black hole indeed to make the effect as small as we measure at the surface of the earth. On the other hand, we can make the effect arbitrarily small by making the box containing the lab arbitrarily small, so there is always some size at which the time dilation between floor and ceiling will be too small to detect.

 

[BenAS]

Strictly speaking, it's not a "difference in gravitational time dilation" that they're measuring, it's the difference between the rates of the two clocks, which is the time dilation. But with that said...

Whether it's greater or less than the effect at the surface of the Earth (which has been measured - google for "Pound-Rebka") will depend on the size of the black hole. The larger the black hole, the smaller the tidal effects across a given distance; but it would take a very large black hole indeed to make the effect as small as we measure at the surface of the earth. On the other hand, we can make the effect arbitrarily small by making the box containing the lab arbitrarily small, so there is always some size at which the time dilation between floor and ceiling will be too small to detect.

Thanks for the reply. So, in theory, the scientists in the lab could tell they were not on the surface of the Earth by measuring the difference in the rates of the clocks?(barring a coincidence, and assuming the lab is the always the same size) And the difference in the rate of the clocks changes as they fall deeper? If so that seems to suggest they could tell they are falling by monitoring the clocks, but I'm having trouble working out if that's true, it would depend on the mass distribution in the black hole?

I'm going to research the math involved, but some of it is over my head.

 

[phinds]

Thanks for the reply. So, in theory, the scientists in the lab could tell they were not on the surface of the Earth by measuring the difference in the rates of the clocks?(barring a coincidence, and assuming the lab is the always the same size)

correct

And the difference in the rate of the clocks changes as they fall deeper?

correct

If so that seems to suggest they could tell they are falling by monitoring the clocks

true

but I'm having trouble working out if that's true, it would depend on the mass distribution in the black hole?

the mass distribution of the black hole is like this: it's all at the center. What he's saying matters is the SIZE of the BH. The bigger the BH, the smaller the tidal gravity at a given distance from the center.

 

[jartsa]

Are you guys really comparing a lab standing on the surface of the Earth and a lab falling into a black hole?

Isn't there the following difference between those two labs:

Inside the lab on the surface of the Earth a clock near the ceiling tends to fall to the floor.

Inside the lab that is falling into a black hole a clock near the ceiling tends to "fall" to the ceiling, because the lab is mostly below the clock, so the lab accelerates faster than the clock, if there is a tidal force.

 

[phinds]

Are you guys really comparing a lab standing on the surface of the Earth and a lab falling into a black hole?

Isn't there the following difference between those two labs:

Inside the lab on the surface of the Earth a clock near the ceiling tends to fall to the floor.

Inside the lab that is falling into a black hole a clock near the ceiling tends to "fall" to the ceiling, because the lab is mostly below the clock, so the lab accelerates faster than the clock, if there is a tidal force.

You right, but no, we were just comparing the clock differentials of a pair of clocks in outer space w/ the same in free fall near a SMBH.

 

[nettleton]

An analysis of what happens on an external item approaches the EH doesn't help my understanding of what happens to internal radiation reaching the EH and the paradox of Hawking radiation allowing a decrease the size of a BH. Hawking suggests outgoing radiation 'hovers' on the internal edge of the EH but that some can escape by a variety of mechanisms such as the Uncertainty Principle that allows velocities >c to exist for short periods of time. I was looking for some means of defining 'hovering'.

 

[phinds]

An analysis of what happens on an external item approaches the EH doesn't help my understanding of what happens to internal radiation reaching the EH

That's not hard. Internal radiation DOESN'T reach the EH, it always goes towards the singularity.

and the paradox of Hawking radiation allowing a decrease the size of a BH.

There's no paradox that I'm aware of.

Hawking suggests outgoing radiation 'hovers' on the internal edge of the EH

He does? I've never heard that. His heuristic description of Hawking Radiation is all about radiation from OUTSIDE the EH, not inside.

but that some can escape by a variety of mechanisms such as the Uncertainty Principle that allows velocities >c to exist for short periods of time.

Another thing I was not aware of but I don't think it is relevant even if true.

 

[mfb]

If you are inside a black hole, all space directions are towards the center. You cannot shine light "outwards" in the same way you cannot shine light "towards yesterday" on Earth.

Hawking suggests outgoing radiation 'hovers' on the internal edge of the EH but that some can escape by a variety of mechanisms such as the Uncertainty Principle that allows velocities >c to exist for short periods of time.

No, not at all.

Hawking radiation is produced outside the black hole.

 

[nettleton]

'Hovers' comes from his 'Black Holes and Baby Universes'. So, if internal radiation propagates back to the centre of the BH, then the mathematically defined EH forms a reflection boundary?

 

[mfb]

No. There is no reflection because the light doesn't even get to it.
To keep the analogy: There is no mirror preventing you from sending light "towards yesterday".

 

[nettleton]

I am slow on the uptake but can't figure out why evaporation external to the EH leads to the BH decreasing in size.

 

[mfb]

The whole system loses energy.

Black holes are not just the singularity. The region around it is important as well.

 

[phinds]

I am slow on the uptake but can't figure out why evaporation external to the EH leads to the BH decreasing in size.

The heuristic explanation (not quite reality) is that a pair of virtual particles pops into existence just outside the EH and before they rejoin, as they normally do, one drops in past the EH and the other escapes to infinity. The one that drops in always has negative energy and decreases the mass of the BH.

 

[Drakkith]

The one that drops in always has negative energy and decreases the mass of the BH.

What about the particle that escapes? It carries away mass from the BH, correct?

 

[phinds]

What about the particle that escapes? It carries away mass from the BH, correct?

No, my understanding is that the one that falls in has negative energy, which decreases the mass of the BH. The escaping one has no effect other than having left its partner behind. REMEMBER, this is a heuristic explanation which Hawking said was the only way he could think of to explain in English some that really can only be explained in the math.

 

[Drakkith]

Well, that mass has to come from somewhere. If not the BH, then where?

 

[phinds]

Well, that mass has to come from somewhere. If not the BH, then where?

My understanding is that the negative energy of the infalling particle removes some of the mass. I've never really worried about it because after all, it isn't what's really happening. It's just an inexact heuristic description of what is really happening

 

[mfb]

it isn't what's really happening

This.
"What would happen if this would be a good model" is not helpful if it is not a good model.