Speed of Swallow of a Black Hole

1. Jan 21, 2014

Nugso

Hello everyone. As far as I know, even lights can not escape from black hole once the light reaches to even horizon as lights carry momentum hence energy. Now, what I wonder is, how fast do black holes swallow light or, if you will, other objects? I guess it cannot be faster than the speed of light, which is $c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}$, because when an object, albeit impossible, exceeds the speed of light it can thus escape from a black hole.

Imagine a pencil being swallowed by a black hole, how fast would that be? Would the object reach the speed of light(which is I guess impossible according to the general relativity but then again accepted laws of physics break down in such circumtances)?

I hope I'm not asking stupid questions. Also I did a search before submitting this, but couldn't find anything.

2. Jan 21, 2014

jcsd

African or European swallow?

3. Jan 21, 2014

Nugso

Are you playing on words or? I don't get it. Was there a verbal mistake?

4. Jan 21, 2014

jcsd

More seriously: there's no such thing as a silly question, but your question is too poorly defined to give a definitive answer. Speed is relative and it also depends on other factors such as initial speed and where the in-falling object starts from.

However we can say that approaching the event horizon though the speed of an in-falling object goes to c relative to a local static observer. This is not because objects cross the event horizon at c in any meaningful sense, it's more an illustration of the impossibility of having a static observer at the event horizon.

5. Jan 21, 2014

jcsd

It was a bad joke (there's a famous scene in Monty Python and the Holy Grail where they discuss the speed of a swallow).

6. Jan 21, 2014

Nugso

Oh, didn't know the movie, sorry. Before I try to explain it in a more clear way, I'd like to know if I get what you said straight. Say, I, as a static observer in the earth observing an object going through event horizon and hence into the black hole, will reach the speed of light? Though, we can't observe because even light gets sucked.

Now, however, what I wanted to say was that how fast does a black hole swallow? For example, if you pull an object with a constant force, there will be change in its speed. We know that F=ma, so it will start to accelerate. I'm merely wondering if such an equation, or a similar one, can be applied to black holes?

7. Jan 21, 2014

jcsd

I'm not sure what you're asking still. A static observer on Earth won't actually observe anything cross the event horizon, the object will actually appear to slow down and approach zero speed as it reaches the event horizon.

There is an equation for the local force required to keep any object static, which diverges at the event horizon, but again I'm not sure if that is what you're asking for.

8. Jan 21, 2014

Nugso

http://www.sketchtoy.com/58465335

What's the force acting on the object, which is due to black hole's 'gravitional force'?

As for your 2nd paragraph, I'd like to know that too if you may.

9. Jan 21, 2014

marcus

Hi Nugso,
http://www.sketchtoy.com/58467472
I tried to make a sketch like yours. I am not accustomed to using sketchtoy and found it difficult, with a touchpad….
Maybe with a mouse it would be easier.

How fast something is going when it crosses the horizon does, I think, depend on how high you drop it from.
Also the effective acceleration at the horizon does, I think, depend on the mass of the BH.
Keep asking questions. I have to go, but will check in later

10. Jan 21, 2014

Nugso

Hi, marcus. Your drawing looks better than mine, though! Say, the earth starts getting sucked into the black hole which is located in the Milky Way. Then the distance/height would be 27.000 light years, and the black hole's mass would be 4 million solar masses. What would be the abovementioned(by you) values? Force acting on the earth, acceleration, speed etc.

I'm going off-topic but I couldn't resist myself from asking this. Can a supermassive black hole swallow an entire galaxy instantaneously? If not, how long would it take?(If it also depends upon the mass of BH which I think it does, suppose the first situation-earth and the black hole in the galactic center-).

Thanks in advance. I've got to sleep. Sorry in case I reply a bit late.

11. Jan 21, 2014

marcus

Your sig quotes Carl Sagan saying "somewhere the sky calls to us. if we do not destroy ourselves we will someday venture to the stars…"
This was set to music by Ken Kristofferson
https://soundcloud.com/kenley-kristofferson/cosmos

"We make our world significant by the courage of our questions and the depth of our answers."

That comes a little later in the 11 minute chorale

Here is a YouTube of a performance at the planetarium in Edmunton (Alberta?) with about 12 singers, Kristofferson conducting, and a keyboard accompanist

The full text (the YouTube has subtitles) has several of Carl Sagan's best quotes

Last edited by a moderator: Sep 25, 2014
12. Jan 21, 2014

phinds

Starting from where? If our galaxy were somehow magically made to stop spinning right now so that everything eventually fell into the black hole, it would take something WAY more than 50,000 years.

How do I get that? Well, it takes light 50,000 years get get from us to it (and we are not even at the edge of the galaxy) and the Earth certainly would not travel at anywhere near the speed of light, at least for quite a bit of the trip.

13. Jan 21, 2014

jcsd

Gravity in general relativity is modeled as the curvature of spacetime. Sufficiently faraway from the black hole's event horizon where the physics are close enough to be being Newtonian and when we can talk about the force due to gravity in terms of the local acceleration required to keep an observer static which is:

$$a = \frac{c^2 r_s}{2r^2 \sqrt{1-\frac{r_s}{r}}}$$

Where $r$ is the radial Schwarzschild coordinate and $r_s$ is the Schwarzschild radius. Note when $r \rightarrow r_s$, $a \rightarrow \infty$; and in the limit as $r_s \rightarrow 0$ the Newtonian expression for acceleration due to gravity is recovered.

14. Jan 22, 2014

Nugso

@phinds, starting from.. all? Assuming the even horizon of a black hole is as large as a galaxy, can it happen in the blink of an eye?

@jscd, So, Say, Mars stopped spinning and gets sucked into the black hole, which is 27.000 light years away, we, as a static observer on the earth, would see it getting accelerated until Mars reaches the event horizon. We can also calculate its speed with the formula you have provided. Now, Mars is in the event horizon, what would be its speed?(infinite?, or if I understood it correcly, it would be 0?)

Last edited by a moderator: Sep 25, 2014
15. Jan 22, 2014

ViperSRT3g

Its speed could be anything you wanted, it's not coming back from beyond the event horizon. (Akin to asking what's outside the universe)

As for objects falling into it, you would see them slowing down, slowly red shifting until it's so red shifted you can't see it anymore.

The reason for this? Imagine the object as it's approaching the black hole's event horizon. It's getting faster and faster approaching c. Throughout this acceleration towards the speed of c, all photons coming from it are already becoming red shifted (they are leaving an object that's moving away from us at nearly the speed of light). Due to relativistic effects, the object is moving so fast, that time is slowing down for it. Thus we see it slowing down, and slowly red shifting.

Now the moment it crosses the event horizon, all photons being emitted from the object will be unable to reach us. So the last thing we see of the object is the object slowing down while red shifting until it's so red shifted you can't see it anymore.

16. Jan 22, 2014

Nugso

I guess I understand a bit better now, but still got a few questions. An object approaching the event horizon accelerate and so does its speed which will approach c. So far so good, now you said its speed could be anything you wanted, and marcus also said something similar(its speed depends on the height), if I crossed the event horizon with 0.99c, what would be my speed as I fall into the singularity?

17. Jan 22, 2014

ViperSRT3g

You could say your speed is as close as you can get to c without actually being c. By that point, it doesn't matter since the object won't leave the black hole again, nor will any of its light.

18. Jan 22, 2014

Nugso

Yes, but I'm merely wondering the velocity of an object falling into a singularity.

19. Jan 22, 2014

ViperSRT3g

It's safe to say that it's as close to c without actually being c.

20. Jan 22, 2014

Nugso

All right, thanks!