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- Thread starter chestycougth
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- #2

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No. Matter inside the event horizon is still timelike. FTL is spacelike.

- #3

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A similar question comes up in an expanding universe, do some objects retreat faster than the speed of light that are passed the cosmic horizon?

It all depends on how you define velocity at a distance in curved spacetime.

Locally it is certainly not falling faster than the speed of light.

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- #4

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If the acceleration caused by gravity is greater than the speed of light at a black hole event horizon[...]

You can't compare acceleration and speed. They have different units.

When you talk about the speed of the infalling object, what is it relative to?

Note that general relativity doesn't offern any meaningful definition of the velocity of an object with respect to a second, *distant* object.

- #5

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Now back to the original question. At the event horizon of a black hole the coordinates are curved so that the T axis points toward the center of the black hole. At this point asking how fast an object is falling is kind of weird because you are asking about a velocity. Velocity has units of distance/time. An object falling through the event horizon is moving along its T axis so this "motion" would have units of time/time, and so is not really motion at all. Therefore a question about the velocity of an object falling into a black hole is a nonsensical question. It's like asking what the color 9 smells like.

- #6

PAllen

Science Advisor

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Now back to the original question. At the event horizon of a black hole the coordinates are curved so that the T axis points toward the center of the black hole. At this point asking how fast an object is falling is kind of weird because you are asking about a velocity. Velocity has units of distance/time. An object falling through the event horizon is moving along its T axis so this "motion" would have units of time/time, and so is not really motion at all. Therefore a question about the velocity of an object falling into a black hole is a nonsensical question. It's like asking what the color 9 smells like.

This last part of your discussion is a coordinate artifact and is not correct. Inside the event horizon, a small region of spacetime is still almost like flat spacetime, with 3 possible orthonormal spatial directions and a time direction that may be defined by the 4-velocity of the infaller (which is still timelike inside the horizon as well as outside and everywhere except being undefined at the singularity). Thus, from the point of view of one infaller, another nearby infaller is moving with a well defined spatial velocity (that can be in any direction), and all sufficiently local physics remains identical to SR.

Another way of looking at this is simply different coordinates. Lemaitre coordinates (as well as Kruskal) have a time coordinate that is everywhere timelike (both inside, on, and outside the horizon), and spatial coordinates that are everywhere spacelike.

What is true is that for a SC geometry, the singularity is spacelike, and all world lines inside the event horizon end on it. For a a rotating BH, neither of these is true - in a Kerr solution there are even stable orbits inside one of the two EH that never reach the singularity.

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- #7

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...If the acceleration caused by gravity is greater than the speed of light at a black hole event horizon...

A free falling observer cannot even detect the event horizon as it is approached and passed...and for such an observer there is nothing unusual at the Schwarzschild radius.

Such an observer continues on their way undisturbed toward the singularity....For a supermassive BH, which may be billions of solar masses in size, the event horizon may be thousands of light years in diameter....In other words, gravity there is rather weak.

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Rather weak but still strong enough to keep whatever fell in inside and not let it escape.

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If the observer free falls from infinity the light from the stars behind him have a frequency of exactly 50%.A free falling observer cannot even detect the event horizon as it is approached and passed...and for such an observer there is nothing unusual at the Schwarzschild radius.

- #10

Bill_K

Science Advisor

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Weeell, not quite. A solar mass black hole has a Schwarzschild radius of about 1.5 km. The relationship is linear, so the radius of a billion solar mass black hole would be a billion km. But a light year is considerably more than that - 10 trillion km.For a supermassive BH, which may be billions of solar masses in size, the event horizon may be thousands of light years in diameter..

(Sorry, it's been a slow day. )

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