# B Speed of light within a black hole

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1. Jan 8, 2017

### 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?

2. Jan 8, 2017

### phinds

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.

3. Jan 9, 2017

### 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.

4. Jan 11, 2017

### 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?

5. Jan 11, 2017

### phinds

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

6. Jan 14, 2017

### Staff: Mentor

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.

7. Jan 14, 2017

### rootone

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.

Last edited: Jan 14, 2017
8. Jan 15, 2017

### BenAS

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)

9. Jan 15, 2017

### Staff: Mentor

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.

10. Jan 15, 2017

### BenAS

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.

11. Jan 15, 2017

### phinds

correct
correct
true
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.

12. Jan 15, 2017

### 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.

13. Jan 15, 2017

### phinds

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.

14. Jan 22, 2017

### 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'.

15. Jan 22, 2017

### phinds

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

There's no paradox that I'm aware of.
He does? I've never heard that. His heuristic description of Hawking Radiation is all about radiation from OUTSIDE the EH, not inside.

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

Last edited: Jan 22, 2017
16. Jan 22, 2017

### Staff: Mentor

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.
No, not at all.

Hawking radiation is produced outside the black hole.

17. Jan 22, 2017

### 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?

18. Jan 22, 2017

### Staff: Mentor

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".

19. Jan 22, 2017

### 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.

20. Jan 22, 2017

### Staff: Mentor

The whole system loses energy.

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