speed of light in a black hole

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hassellhoff
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speed of light in a black hole

Postby hassellhoff » Wed Dec 31, 2008 12:30 am UTC

just a quick question here, if not even light can escape a dark hole, then theoretically, couldnt a dark hole make matter move faster than the speed of light?
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Re: speed of light.

Postby thoughtfully » Wed Dec 31, 2008 12:34 am UTC

no
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Re: speed of light.

Postby Klotz » Wed Dec 31, 2008 12:57 am UTC

No. If something is inside a black hole, then going towards the centre is the same as going forwards in time, and trying to escape is the same as going back in time.

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Re: speed of light.

Postby danpilon54 » Wed Dec 31, 2008 1:44 am UTC

it's not obvious without general relativity, a subject about which I know almost nothing, being a lowly undergrad.
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Re: speed of light.

Postby Xanthir » Wed Dec 31, 2008 4:33 pm UTC

hassellhoff wrote:just a quick question here, if not even light can escape a dark hole, then theoretically, couldnt a dark hole make matter move faster than the speed of light?

Others have already said no, and Klotz gave a decent explanation, but let me give another.

Have you heard that mass distorts space? This is essentially general relativity. One way of thinking about gravity is that mass distorts space, so that a straight line through space becomes curved (specifically, straight lines curve toward the massive objects, which is how gravity works). Slow things have their paths curved enough that they'll hit the massive objects, but fast things have their paths curved less so they just get slightly diverted.

A black hole is black because it curves space *so much* that even paths pointing directly away from the center of the black hole curve all the way around back to the center again. Even things travelling at maximum speed (speed of light) have to follow these paths, so light can't escape. No matter which way you turn, moving forward means that you're heading toward the center.

(You may see that this is equivalent to what Klotz said. There's actual math linking the two explanations, but it's complicated.)
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Re: speed of light.

Postby thoughtfully » Wed Dec 31, 2008 5:24 pm UTC

The clearest explanation for the speed of light as an ultimate limit is that in four dimensional spacetime, everything has the same "speed". You can divide up the space and time components however you like, but you can't exceed the fixed speed. For instance, a massless particle, such as a photon, traveling at the speed of light, experiences no passing of time, and has no component in the time dimension. This is another way of visualizing time dilation.
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Re: speed of light.

Postby Rentsy » Wed Dec 31, 2008 6:47 pm UTC

Or you could just say that a black hole exerts a force on matter, and no matter what kind of force, it doesn't matter, because you can't go faster than the speed of light.

Why is that though? We all know it. We all "know" light is the cosmic speed limit.

[math]p = \frac {mv}{\sqrt{1-\frac{v^2}{c^2}}}[/math]

Where m and v are the nonrelativistic mass and momentum, p is, and c is the speed of light (celeritas)

Anyhoo, as a thing goes faster, it's momentum increases. We see this with small, high energy particles being more reluctant to be nuged than we'd expect in a non-relativistic world.

This is because their mass is, actually, increasing, the faster they go.

Now, having more mass makes you harder to push. So an imaginary rocket ship designed to fly at c, having enough fuel to do so, would run into problems at ~70.7% of the speed of light, as the ship now weighs twice as much as it "ought", and thus puts up twice as much resistance to being pushed. And so on and so on the closer to c you get, the harder you are to accelerate.

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Re: speed of light in a black hole

Postby IIAOPSW » Fri Jan 02, 2009 3:43 pm UTC

3*10^8 m/s...the speed of light is the same to all observers! If we consider the speed of light in a black hole to be 0 relative to an observer on the outside then gravitational time dilation fixes everything.1 second out of the hole is equal to forever I'm or.
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Re: speed of light.

Postby gmalivuk » Fri Jan 02, 2009 11:02 pm UTC

Rentsy wrote:Or you could just say that a black hole exerts a force on matter, and no matter what kind of force, it doesn't matter, because you can't go faster than the speed of light.

But this is a hand-wavy and incomplete answer. The same theory that shows you can't go faster than light gives you a much better, geometric explanation of why it's not even sensible to talk about escaping from within the event horizon of a black hole, and it's really got nothing to do with acceleration or forces.

Within the event horizon, *all* future timelike and null paths (those followed by matter and photons, respectively) point towards the center of the hole.
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Re: speed of light in a black hole

Postby Rentsy » Sat Jan 03, 2009 12:38 am UTC

But, gmalivuk, explanations like that might be *true* in the strictest sense of the word, but it doesn't explain anything. What's a "null path"?

By the way, what's hand-wavy about saying that a force, however great, cannot cause a thing to exceed the speed of light? Black holes don't operate on magic, as far as I know. I know they cause some weird stuff to occur, I know that information is not destroyed, but never have I ever heard anything about going faster than light.

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Re: speed of light in a black hole

Postby doogly » Sat Jan 03, 2009 6:52 am UTC

Rentsy wrote:I know that information is not destroyed


I'd like to suggest that you don't know this, but perhaps I missed some major announcement?

Null paths have length zero, and are the paths photons take in a vacuum. Are you familiar with metrics? That is where you would get this length from. If you take a (-+++) signature, then timelike paths are the ones with negative length. You are also likely from the east coast. Represent.
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Re: speed of light.

Postby Cryopyre » Sat Jan 03, 2009 7:25 am UTC

thoughtfully wrote:The clearest explanation for the speed of light as an ultimate limit is that in four dimensional spacetime, everything has the same "speed". You can divide up the space and time components however you like, but you can't exceed the fixed speed. For instance, a massless particle, such as a photon, traveling at the speed of light, experiences no passing of time, and has no component in the time dimension. This is another way of visualizing time dilation.


So like a ratio of 1/0, it is undefined, and infinity in our universe is C?
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Re: speed of light.

Postby doogly » Sat Jan 03, 2009 7:32 am UTC

Cryopyre wrote:
thoughtfully wrote:The clearest explanation for the speed of light as an ultimate limit is that in four dimensional spacetime, everything has the same "speed". You can divide up the space and time components however you like, but you can't exceed the fixed speed. For instance, a massless particle, such as a photon, traveling at the speed of light, experiences no passing of time, and has no component in the time dimension. This is another way of visualizing time dilation.


So like a ratio of 1/0, it is undefined, and infinity in our universe is C?


Nope. Light paths have just as much time separation as they do space separation, so that the total length along such a path is zero; for flat space, s^2 = -t^2 + x^2. For anything besides light, you travel through less space in more time. It isn't correct to say that light's momentum has no component in the time direction.
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Re: speed of light in a black hole

Postby Rentsy » Sun Jan 04, 2009 3:13 am UTC

These "explanations" make no sense to an intelligent, but uneducated reader. I have no idea what you are talking about, Mr. doogly. Maybe it is the fact I live on the West Coast?

Cyropyre, you however, I can try to help.

c is not infinity. c is the "speed limit". The fact that the laws of nature seem to be elaborately devised to constrain ourselves are due to the LAW that we cannot determine absolute motion. Everything else falls out of this.

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Re: speed of light in a black hole

Postby doogly » Sun Jan 04, 2009 4:55 am UTC

Rentsy wrote:These "explanations" make no sense to an intelligent, but uneducated reader. I have no idea what you are talking about, Mr. doogly. Maybe it is the fact I live on the West Coast?

Cyropyre, you however, I can try to help.

c is not infinity. c is the "speed limit". The fact that the laws of nature seem to be elaborately devised to constrain ourselves are due to the LAW that we cannot determine absolute motion. Everything else falls out of this.


Yeah, the west coasters take a (+---) signature. It's ridiculous.

So, you are not familiar with metrics? I'll take a step back then. A metric is a way of defining distance. The distance is s, and the d means "tiny differential piece of." The standard distance element in flat 3 space is the Cartesian one:
[math]ds^2 = dx^2 + dy^2 + dz^2[/math]
We could, if we so chose, put flat space in different coordinates.
[math]ds^2 = dr^2 + r^2 d\phi^2 + r^2 sin^2(\phi)d\theta^2[/math]
This isn't the definition of distance on a 3 dimensional sphere though - it is in flat space but with coordinates that slice up space into 2 dimensional spheres indexed by r. The whole space is still flat. For a 3-sphere the distance element is
[math]ds^2 = d\psi^2 + sin^2(\psi)\left(d\phi^2 + sin^2(\phi)d\theta^2\right)[/math]
These are all for spaces with a purely positive definite metric. No distance is ever negative, and the only time s=0 between two points is when they are actually the same point. But! To include time, you give the time coordinate a different sign. So, for special relativity, which takes place in flat space, you have
[math]ds^2 = -dt^2 + dx^2 + dy^2 + dz^2[/math]
Or, if you like,
[math]ds^2 =-dt^2+ dr^2 + r^2 d\phi^2 + r^2 sin^2(\phi)d\theta^2[/math]
And you can cook up coordinates that mix up the time and space, like what are called radial null coordinates. Define u=(r-t), v=(r+t), and then the metric for flat space (exactly the same as special relativity, new coords only) becomes
[math]ds^2 = dudv + \frac{(u+v)^2}{4} \left(d\phi^2 + r^2 sin^2(\phi)d\theta^2\right)[/math]

And so! This is what distance means. If two points are a distance zero apart, they are null separated, if the distance is greater than zero they are spacelike, and if less than zero, timelike.

If you've done things like figure out what the volume element you need to integrals in different coordinates is, or that kind of problem, you've been using related sort of stuff. Is any of that familiar?

Some caveats: I totally set the speed of light equal to one. Everywhere I wrote dt^2 you could pretend it says c^2dt^2, or else get comfy measuring time in units of millimeters. No reason why not to. Also, I haven't told you what a metric is yet: a sloppy physicist would tell you it is the matrix [imath]g_{ij}[/imath] such that [imath]ds^2=\Sigma_{ij}g_{ij}dx_i dx_j[/imath] But the matrix is just the components of the metric, not quite right. But I'm just a nonsloppy physicist, not a mathematician, so I can assure you thinking that matrix is the metric is good enough.
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Re: speed of light in a black hole

Postby Senefen » Wed Jan 07, 2009 4:19 am UTC

Nope, light moves at light speed, you'd think it would pull things in faster but time slows down with high speeds and intense gravity so the object is still travelling below light speed thanks to time distortions and light is still travelling at light speed.

Interestingly the maths says you can't push beyond light speed but if you manage to create a particle that is travelling above light speed when it's created you'll never be able to slow it to below light speed. It's a hyperbola, so you get stuck on either side of it (with mass). While light speed sits as the asymtope.
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