# Speed of light = oo mass = black hole?

1. Dec 16, 2011

### MassiveMass

So I'm new to this, but it's one hobby that fascinates me. I figured I'd come here to listen to your thoughts. I was thinking the other day about an alternative energy and naturally "too bad we can't tap into a quasar" came up. For now I think the thermosphere seems to be the biggest source of raw clean energy here.

Here it is. What if you harnessed "some of Super Conductor of the future". Then with this Mega Massive super conductor you found "some way of utilizing power from a quasar". This is all a little out there so bear with me but this is the kind of energy you'd want to actually test this theory in theory. We'd then use that energy to power a large spacecraft that could accelerate stably to near or if say we could in theory travel fast enough to catch up with light." Now present day we believe this to be almost impossible. Now lets say in theory they are wrong. Well that ship when it reached the speed of light. Here's the question. When we reach this speed of light and our density in theory reaches the critical point would matter implode on itself? Maybe creating a small black hole or singularity like when an incredibly dense star collapses on itself after the white dwarf stage and creates a gravitational vacuum. Well I don't think it defies physics anyway, but some do. I just think there's some point like the speed of light which i think is the "speed of time or how we measure it, but also a max density as well or some sort of critical mass or the point where matter implodes because it's so dense. I'm just curious about these things.

Then there's time. Does the object appear to be moving at a standstill to an outside observer or more likely vice versa based on relativity. Wouldn't that kind of gravity at the speed of light warp time itself so what would that look like to an observer coupled with the standstill. Please help me educate myself in this.

Thanks.

2. Dec 16, 2011

### mathman

When something gets close to the speed of light, relative to us, the mass appears very large to us. However in the reference frame of the object itself the mass is still the rest mass.

3. Dec 16, 2011

### Staff: Mentor

4. Dec 17, 2011

### MassiveMass

Hey thanks for the help that makes way more sense. Just to be clear. A small object with low density moving very fast doesn't have more gravity then objects of higher density not moving at all. If I'm off just let me know. Thanks.

5. Dec 17, 2011

### Elroch

An object with little mass moving fast does have a greater gravitational influence, but it is because it has momentum: Einstein's equation says roughly that curvature of space-time is proportional to a thing called the stress-energy tensor. One of the components of this tensor comes from mass, all the others derive from momentum. An extreme example is light, which has zero rest mass, but does have momentum and does have a gravitational influence.

6. Dec 17, 2011

### MassiveMass

That's what I'd previously understood. So the stress-energy tensor is how we actually measure gravitational pull. I did not know that. So then at what factor does the stress-energy tensor become large enough for a black hole? I.E. (put warp drive on a planet for example and accelerate with the energy of a quasar etc. etc.). What is the point at which we reach singularity? Are there other ways to reach singularity?

7. Dec 17, 2011

### Naty1

Post 5 and 6 above are incorrect statements and conclusions.

A long discussion is here:

For a quick perspective, see my post #5 and PeterDonis post #10.

Going faster does NOT offer the opportunity for anything to turn into a singularity, that is, a black hole. Gravity is the only force strong enough to create a black hole and does NOT work that way.

8. Dec 17, 2011

### Elroch

Naty1, you claimed my post was incorrect: please specify precisely to which statement you were referring unless you posted in error.

I stand by my statements.

Specifically, the momentum of a body affects its gravitational influence. The clearest example of this is light, which has zero rest mass, but which obviously causes curvature of space time according to Einstein's field equation.

Note that whether something forms a black hole is obviously independent of the frame of the observer, so is not affected by changes of relative velocity, for example.

9. Dec 17, 2011

### Matterwave

I've always found this FAQ inadequate. It sort of just says "no, but the reasons are complicated". It also implies (I think, through it's rather vague language) a 1 to 1 equivalence of black holes and singularities. Now, I'm not an expert on the singularity theorems of Hawking and Penrose, but I do know that the so called "cosmic censorship conjecture" is simply a conjecture, and therefore naked singularities at least have not been proven to not exist. There is therefore not a 1 to 1 equivalence between a singularity and a black hole. Do the singularity theorems say that for every blackhole there is a singularity?

Since the curvature is expressed as a tensor, the components of which are obviously dependent on the coordinate system used, and therefore the frame of reference, it seems to me that the only thing we can say for sure is that a singularity does not form. Obviously since a singularity implies an incomplete geodesic, it cannot exist in one FoR and not exist in another. What about a black hole?

@Elroch: Because the curvature is expressed as a 256 component tensor (the Reimann), it's not so easy to just make a statement like "gravity increases". Which component are you talking about? The Einstein Field equations only specify the trace of the Reimann (the Ricci tensor basically), but do not specify the traceless part of the Reimann (the Weyl tensor). The traceless part is determined in some way by (some sort of global) boundary conditions.

Outside a distribution of mass (in the vacuum), it is only the Weyl curvature which survives. It doesn't seem legitimate to me, then, to say that the "stress energy increases therefore gravity increases" since in the vacuum region, the stress energy tensor is 0 for both a moving or non-moving mass. If you are in the "interior region" where the stress energy does not vanish, then you are obviously moving along with the particle, and not in a FoR where the particle is moving at great speeds.

10. Dec 17, 2011

### Elroch

Thanks Matterwave, a helpful and informed post which makes me realise how far from complete my understanding is! My wording was (partially intentionally) very loose, indicating merely that momentum contributes to the gravitational field. My understanding is that the curvature resulting from the stress-energy is the source of the large scale gravitational characteristics (metric structure?) in the region outside the matter. For example, orbit period. Is this correct?

It seems trivially obvious that changing your velocity won't turn you into a black hole. How can your velocity have any effect, since you and your physical behaviour are always the same in any frame at rest w.r.t to you?

Last edited: Dec 17, 2011
11. Dec 17, 2011

### Staff: Mentor

Or look at it this way: we can increase my velocity relative to you either by accelerating me, or by accelerating you. Suppose we do the latter. How can your acceleration turn me into a black hole?

12. Dec 19, 2011

### Naty1

Elroch and Matterwave: Curvature and gravity is waaay more subtle than I thought when I started in these forums.....
I've made notes from posts over several years and pieced together what may help you as it did me:

is incorrect:

You should read Peter Donis explanation which I referenced above...
"Does mass really increase with speed"

except the posts are # 10, #16.....

PeterDonis:
This is the correct idea:

[QUOTE... changing your velocity won't turn you into a black hole. .....you and your physical behaviour are always the same in any frame at rest w.r.t to you?......Note that whether something forms a black hole is obviously independent of the frame of the observer, so is not affected by changes of relative velocity, for example.[/QUOTE]

also:
likely you mean VELOCITY.

I found a different post from Peter which is close to what was referenced above:

And one of my favorite explanations relates two types of CURVATURE:

The key is that gravitational curvature IS observer independent (as already noted) and is reflected as curvature of the spacetime manifold ("graph paper" as described below). Frame dependent curvature (observer dependency) is a variable overlay on top of this fixed background curvature,

From Dr Greg:

Last edited: Dec 19, 2011
13. Dec 19, 2011

### Staff: Mentor

Light does cause spacetime curvature, but this is due to its energy and pressure, not its momentum.

14. Dec 19, 2011

### Naty1

By now, it's likely clear that acceleration and velocity do not cause an increase gravity. They do cause an apparant ...frame dependent....curvature separate from gravity.

http://en.wikipedia.org/wiki/Black_hole#Gravitational_collapse

Gravitational collapse results in a singularity accompanied by a black hole .....and event horizons of various sorts.

15. Dec 19, 2011

### Matterwave

Which parts of my post are you critiquing specifically? I tried to look for quotes from me but I couldn't find any.

16. Dec 20, 2011

### harrylin

Yes, I think that that is the best (simple, straightforward and relativistic) explanation.

PS it is mentioned in there, but in a weak form; it's not stressed that this must be so according to relativity theory.

17. Dec 20, 2011

### Staff: Mentor

Post 5 was good except for one small nitpick:
Here "mass" should be "energy". Other than that minor detail it is fine. I would also probably say "different" gravitational influence rather than "greater", but I am sure that you could justify "greater" in some coordinate systems.

18. Dec 20, 2011

### Staff: Mentor

No, the Riemann curvature tensor represents gravity. The stress-energy tensor is the source of gravity. I.e. in Newtonian mechanics the source of gravity is mass, but in GR the source of gravity is a tensor comprised of energy, momentum, pressure, and stress.

It doesn't. As you go faster your energy increases, but so does your momentum. Those two work together to prevent a horizon from forming.

19. Dec 20, 2011

### Staff: Mentor

This is a good and well-reasoned question. Consider null geodesics in the rest frame of some non-black hole object. Those geodesics all escape to an asymptotically flat region. Now, apply a boost such that the object is moving at relativistic speeds. The null geodesics in the original frame remain null geodesics in the new frame and escape to an asymptotically flat region. Therefore the object is not a black hole.

20. Dec 20, 2011

### Staff: Mentor

Since light has momentum then it has some corresponding non-zero components in the stress energy tensor, and therefore by the EFE it does cause spacetime curvature due to its momentum also.