The speed of light remains constant at c, even near the event horizon (EH) of a black hole, as established by general relativity. Observers outside the EH perceive light as redshifted, but this does not affect its speed. Inside the EH, light emitted from a source, such as a flashlight, travels at c until it reaches the singularity. The effects of gravitational time dilation and tidal forces vary depending on the size of the black hole, impacting measurements of time and light within a falling laboratory.
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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.nettleton said: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?
No. If you turn on a flashlight inside the EH, it emits photons at cnettleton said:Am I to assume that light is not generated within the black hole but only close to the E.H.?
No, light escaping from the environs of an EH arrives at c, just red shifted. Read post #2.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.nettleton said: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?
Will put that on my list of things to do.Nugatory said: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 ...
Nugatory said: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.
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...BenAS said: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?
Nugatory said: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.
correctBenAS said: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)
correctAnd the difference in the rate of the clocks changes as they fall deeper?
trueIf so that seems to suggest they could tell they are falling by monitoring the clocks
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.but I'm having trouble working out if that's true, it would depend on the mass distribution in the black hole?
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.jartsa said: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.
That's not hard. Internal radiation DOESN'T reach the EH, it always goes towards the singularity.nettleton said: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
There's no paradox that I'm aware of.and the paradox of Hawking radiation allowing a decrease the size of a BH.
He does? I've never heard that. His heuristic description of Hawking Radiation is all about radiation from OUTSIDE the EH, not inside.Hawking suggests outgoing radiation 'hovers' on the internal edge of the EH
Another thing I was not aware of but I don't think it is relevant even if true.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.nettleton said: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.
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.nettleton said:I am slow on the uptake but can't figure out why evaporation external to the EH leads to the BH decreasing in size.
phinds said:The one that drops in always has negative energy and decreases the mass of the BH.
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 said:What about the particle that escapes? It carries away mass from the BH, correct?
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 happeningDrakkith said:Well, that mass has to come from somewhere. If not the BH, then where?
This.phinds said:it isn't what's really happening