What Causes a Star to Collapse into a Black Hole?

[TalonD]

I have an idea why, but would like to know if there are any official 'theories' ?
also, I can think of an idea of why the speed of light is 300k kilometers in vacuo, but is there an 'officially' accepted theory? I havn't found any in the literature.
thanks Talon D.

 

[MeJennifer]

I have an idea why, but would like to know if there are any official 'theories' ?
also, I can think of an idea of why the speed of light is 300k kilometers in vacuo, but is there an 'officially' accepted theory? I havn't found any in the literature.
thanks Talon D.

The only thing we can say is that light has a definite fixed speed. The value of this speed depends entirely on the chosen units of measurement.

 

[TalonD]

light has an absolute speed regardless of the unit of measurment. My question is why is it that speed and not for example twice that speed or half that speed. The answer seems obvious of course. There is nothing special about light itself, what is special is the speed limiit. Which I think is determined by certain properties of space and time since speed is a measurement of distance over time. I could get into some detail but that would be too much speculation. As for my other question, why does mass bend space, the answer to that one also seems obvious but again that would entail a good deal of speculation. I was just wondering if there was any mainstream answers. Since I've never stumbled across them, they must be rather obscure or non existent. Which is strange considering the fundamental nature of such questions.
I notice the forum rules forbid wild speculation so I will refrain. :P

 

[MeJennifer]

light has an absolute speed regardless of the unit of measurment. My question is why is it that speed and not for example twice that speed or half that speed.

I do not think your are getting it. If the speed is say x, then it is x because of the chosen units of measurements. For instance it would be 1, 2x, 1/2x, 5x etc if you were to take other units of measurements.

Another example: Why is a certain amount of gold exactly 1 kg? Why not 2kg or 1/2kg? Again that entirely depends on the units of measurements.

 

[TalonD]

I do not think your are getting it. If the speed is say x, then it is x because of the chosen units of measurements. For instance it would be 1, 2x, 1/2x, 5x etc if you were to take other units of measurements.

Another example: Why is a certain amount of gold exactly 1 kg? Why not 2kg or 1/2kg? Again that entirely depends on the units of measurements.

without trying to be too argumentative I don't think you understand my question. it doesn't matter if you are using miles per second or kilometers per second or lightyears per century, the unit of measurement you are using is arbitrary and does not change how fast the light is actually traveling through a vacuum. if you choose kilometers per second for example. and you measure the speed of light with some experimental aparatus, you will always get the same 300 thousand kilometers(rounded) per second in a vacuum. you will never measure it going 400 k per second or 50 kilometers per second in a vacuum, unless you have a faulty experimental aparatus.

as for the gold... how many kg it weighs depends on the mass of the planet that you are wieghing it on. On Earth it has a certain weight because the Earth has a certain mass and therefore a certain gravitational field strength and so does the gold. After all, it would weight less on the moon than it does on the Earth. So a better question would be why does the gold have the mass that it has? The answer of course is because it's atoms are composed of neutrons, protons and electrons, each of which has a certain mass and are packed into a certain volume which gives the gold its mass per volume. so the real question is why does the newtron et al have any mass at all? is it because of the Higgs boson or something? and around we go back to one of my original two questions, why does mass cause space to bend? did I get a little off topic? :P sorry.

 

[marcus]

without trying to be too argumentative I don't think you understand my question. it doesn't matter if you are using miles per second or kilometers per second or lightyears per century, the unit of measurement you are using is arbitrary and does not change how fast the light is actually traveling through a vacuum. ...... why does the gold have the mass that it has? ...because it's atoms are composed of neutrons, protons and electrons, each of which has a certain mass and are packed into a certain volume which gives the gold its mass per volume. so the real question is why does the newtron et al have any mass at all? ...why does mass cause space to bend? ...

Jennifer and Talon, if either of you think you are getting off into a tangential disagreement that is primarily about words, I don't think anyone would think the less of you if you just abandoned whatever doesn't relate to Talon's declared topic----by what mechanism does mass affect geometry?

Talon, I don't have much hope because everybody would like to think of a mechanism for matter to cause curvature----no one has been able to so far----and if someone did, still in science some 95 percent of people's ideas turn out wrong, an overwhelming percentage of theory gets discarded because it either can't be empirically tested or else it fails the test.

But if you have an idea, Talon, you had better go right ahead and present it. One of the staff may decide, upon consideration, that it belongs in the Independent Research forum, which is all right. But for starters we have no idea what you have in mind.

There is a branch of research called quantum gravity which ultimately is aimed at finding a mathematical model of the microscopic fundamental descriptors of both matter and geometry (they may be two aspects of th same thing) and ultimately aims to explain how matter and geometry interact. Hundreds of people would love it if they could make some historical breakthru there. We could understand extreme situations like the pit of a black hole or the conditions at the beginning of expansion. But so far no breakthru.

Whatever mechanism you have in mind probably should explain not only how energy density can affect geometry but also how PRESSURE can. Part of the gravitational attractiveness of the sun is actually due to the pressure at the core. Anyway that is what General Relativity says. there is the mass, which you know about, and the mass density which can be converted to an energy density by the usual equivalence.

and energy density (or equivalent mass density) does indeed affect geometry as we all know. but also the GR equation says that the pressure also has an effect------typically not very much because the energy density term is so much larger, but still some effect.

anyway it is a hard problem and it is a gamble thinking about it, with very long odds, but if you have mechanism that you want to describe it seems appropriate to make a stab at it, don't keep us in suspense

 

[MeJennifer]

as for the gold... how many kg it weighs depends on the mass of the planet that you are wieghing it on.

No it does not.

At any rate this is tangent to the topic at hand so I refrain from further arguments about this.

 

[Ynaught?]

No it does not.

Sure it does. TalonD even went on and explained why.

@TalonD - While not mentioning Higgs, I think Marcus did pretty well with your first question. I think the answer to your second is much more straightforward... have you heard of Maxwell? $$c=\sqrt{\frac{1}{\epsilon{0}\mu_{0}}$$

 

[MeJennifer]

Sure it does. TalonD even went on and explained why.

A bar of gold of 1 kg is 1 kg regardless whether it is placed on a small or a heavy planet. A kg is the SI base unit of mass not weight. Perhaps TalonD does not realize the difference between mass and weight.

 

[Ynaught?]

A bar of gold of 1 kg is 1 kg whether it is placed on a small or a heavy planet. A kg is the SI base unit of mass.

True. But if you want TalonD to be clear and say "how much a kilogram meter per second squared of gold weighs?" than just say so. It seems pretty clear to me that that is how he read your statement about "amount of gold"... And then he went on to clarify

So a better question would be why does the gold have the mass that it has?

which is what you meant in the first place... Again, I think Marcus had it right; the tangential argument over semantics is just that.

*EDIT - Looks like you were editing while I was replying. ;)

 

[oldman]

I have an idea why, but would like to know if there are any official 'theories' ?
Talon D.

No, there aren't, as marcus has pointed out.

It may help to realize what people are trying to do here. They are trying to predictively describe gravity, integrated with the other physical interactions of nature, with the help of an invented language, mathematics. We do this just because we can --- we are driven to talk, discuss and chatter endlessly about future happenings by our very nature. Predictive talk helps our fitness to survive. I'm talking evolutionary stuff here.

Such talk means answering as many "how" (rather than "why") questions as we can. Saying "mass bends space' is the best (most predictive) way of describing gravity anybody has found yet. But it's only today's description; tomorrow's may be deeper, more integrated with other knowledge and more predictive.

Perhaps your idea will lead on to such an improvement? What is it?

 

[stevebd1]

While it doesn't necessarily relate to the curvature of space, I saw a description of mass in another thread, describing it as a resistance to acceleration. According to the Higgs mechanism, everything wants to travel at the speed of light but some particles are suppressed by the Higgs field, fermions 'tumble' through the field and are seen as matter while bosons skim across the field and are basically invisible. Maybe this resistance to acceleration goes some way towards explaining curvature?

 

[Fredrik]

I have an idea why, but would like to know if there are any official 'theories' ?
also, I can think of an idea of why the speed of light is 300k kilometers in vacuo, but is there an 'officially' accepted theory? I havn't found any in the literature.
thanks Talon D.

The answer to both questions would have to be a theory that replaces general relativity as the "best theory so far" of gravity, and the answer to the second question would probably also have to be a theory that includes quantum phenomena (especially if you want the new theory to tell us the value of c as a function of $\hbar$ and other constants of nature). There are no such theories yet.

 

[TalonD]

MeJennifer, you are right on both counts. About the kilo of gold, I get used to thinking of a kilogram as a unit of weight measurement probably due to my bathroom scales.. 79.3 this morning, time to go on a personal mass reduction plan. :) after re-reading, I see that I was misinterpreting your response. I stand corrected. ok, that expired equine has been flailed enough.

Perhaps 'obvious' was the wrong word to use. It implies that I actually have the right answer. After all it is 'obvous' that the Earth is flat to someone who doesn't know any better so I don't put much stock in the obvious :P As Marcus says, most theory is discarded and wrong, and being a nearly clueless rank amateur, my ideas would most probably fall into that category. I don't take myself very seriously and the rest of you shouldn't either.

the speed of light constrained by quantum properties of space and time, and gravity caused by an interaction of the geometry and expansion of space time and the resistance of mass to a change in motion.

briefly, too busy, more later

 

[azzkika]

Whatever mechanism you have in mind probably should explain not only how energy density can affect geometry but also how PRESSURE can. Part of the gravitational attractiveness of the sun is actually due to the pressure at the core. Anyway that is what General Relativity says. there is the mass, which you know about, and the mass density which can be converted to an energy density by the usual equivalence.

and energy density (or equivalent mass density) does indeed affect geometry as we all know. but also the GR equation says that the pressure also has an effect------typically not very much because the energy density term is so much larger, but still some effect.

anyway it is a hard problem and it is a gamble thinking about it, with very long odds, but if you have mechanism that you want to describe it seems appropriate to make a stab at it, don't keep us in suspense

does this mean that 2 equal masses of different denseness will cause different space curvature??

 

[marcus]

does this mean that 2 equal masses of different denseness will cause different space curvature??

well first let's ask if it is true or not! Is it true that 2 equal masses can cause different curvature?
Yes, it is certainly true. Just think about the sun versus a neutron star with the same mass as the sun. Consider a point which is 100 km from the center. At 100 km from the center of a neutron star the gravitational field is very strong. At 100 km from the center of the sun it is not so strong. So the density makes a big difference in the curvature.

Much farther away from center I don't suppose you would notice any difference. Assuming they really have the same mass. The effect of pressure is included in determining the mass and is normally slight.

 

[stevebd1]

Isn't Einsteins equation for gravity g=ρc²+3P (basically energy density plus 3 times the pressure)-

The equation for Newtonian gravity being (incorporating m=V/ρ)-

$$g=G\frac{m}{r^2}=G\frac{4\pi r_0^3}{3r^2} \rho$$

where G is the gravitational constant, r₀ is the radius of the object of mass, r is the distance between the center of the object and the point at which gravity is being calculated and ρ is the density of the object of mass in kg/m^3 (Note when calculating gravity at the surface, r₀^3/r^2 can be reduced to simply r₀)

and the equation for GR gravity being-

$$g=G\frac{4\pi r_0^3}{3r^2} \left(\rho+\frac{3P}{c^2}\right)$$

as above but where P is pressure in N/m^3 and c is the speed of light

As Schwarzschild metric is relative to m, would Schwarzschild metric also incorporate P?

 

[MeJennifer]

As Schwarzschild metric is relative to m, would Schwarzschild metric also incorporate P?

Since the Schwarzschild solution is a vacuum solution there is no pressure involved.

 

[stevebd1]

Thanks Mejennifer, I had a suspicion it might not. I only ask because Schwarzschild metric appears to be the measure of the curvature of space in a vacuum caused by the gravity of an object and while it is a vacuum solution, m in the equation might have been replaced with $V(\rho+3P/c^2)$ as the mass of the object would appear to increase due to pressure which might have had an indirect effect on curvature.

What about escape velocity. Is there any evidence that pressure might be incorporated into the escape velocity equation, $v_e=\sqrt{2gr}$?

 

[stevebd1]

I understand that while gravity is the curvature of space and is based on active mass, $V(\rho+3P/c^2)$, coordinate acceleration is the curvature of spacetime and appears to be simply based on (inertial?) mass, $V\rho$. While it's been stated that Schwarzschild metric is a vacuum solution and that pressure is not involved, can anyone explain in more detail why M, the mass in Schwarzschild coordinate acceleration, does not incorporate the pressure of the mass also (i.e. active mass)?

Here's a couple of interesting paragraphs about the effects of pressure in GR-

The meaning of Einstein's equations-
math.ucr.edu/home/baez/einstein/einstein.pdf page 7, section gravitational collapse.

Astrophysical Cosmology 4-
www.roe.ac.uk/japwww/teaching/cos4notes/notes.pdf page 16, section 5.5 effects of pressure

According to the first paper, it states that pressure contributes to the collapse of a neutron star into a black hole which implies that the pressure in matter has some effect on the escape velocity.

 

[MeJennifer]

While it's been stated that Schwarzschild metric is a vacuum solution and that pressure is not involved, can anyone explain in more detail why M, the mass in Schwarzschild coordinate acceleration, does not incorporate the pressure of the mass also (i.e. active mass)?

M is modeled as a point mass in the Schwarzschild solution. Point masses are problematic in GR as the energy-momentum tensor blows up. Only when you have a region of mass-energy could you potentially model the effect of pressure as such regions are not Ricci flat.

Would the singularity exist if we would not assume a point mass and asymptotic flatness at infinity?

 

[atyy]

I can think of an idea of why the speed of light is 300k kilometers in vacuo, but is there an 'officially' accepted theory? I havn't found any in the literature.
thanks Talon D.

There is no "officially" accepted theory. However, there are speculations made by "official" physicists.

The value of the speed of light itself depends on our choice of units - for example, we get a different number for the speed of light depending on whether we measure it in inches or meters. However, the speed of light can be combined with other quantities to form numbers that don't depend on our choice of units. It is about these numbers that some "official" physicists speculate about. For example, some people speculate that the value of those numbers depends on the age of the universe.

All these guys disagree with each other, but I think all of them qualify as "official" physicists.
http://arxiv.org/abs/physics/0110060

 

[atyy]

As for why mass causes space to bend, again there are no "official" theories, but there are speculations by "official" physicists. Again, some examples.

http://arxiv.org/abs/0712.0427
http://arxiv.org/abs/gr-qc/0606100
http://arxiv.org/abs/hep-th/0611197

 

[stevebd1]

M is modeled as a point mass in the Schwarzschild solution. Point masses are problematic in GR as the energy-momentum tensor blows up. Only when you have a region of mass-energy could you potentially model the effect of pressure as such regions are not Ricci flat.

Thanks for the reply, MeJennifer. So basically while the gravity field is a http://en.wikipedia.org/wiki/Stress-energy_tensor" which means m is based on point mass (no volume, no density and therefore no pressure to incorporate).

Steve

 

[stevebd1]

Hopefully this isn't too off topic but while metric is based on point mass, escape velocity looks like it relates directly to active mass based on the fact that g can be incorporated into the equation.

$$\tag{1}v_e=\sqrt{\frac{2Gm}{r}}=\sqrt{2gr}$$

which raises the issue of the possible effects of pressure on the collapse of the star into a black hole-

'There are a number of important situations in which ρ does not dominate P. In a neutron star, for example, which is held up by degeneracy pressure of the neutronium it consists of, pressure and energy density contribute comparably to the right-hand side of Einstein's equation. Moreover, above a mass of about 2 solar masses a nonrotating neutron star will inevitably collapse to form a black hole, thanks in part to the gravitational attraction caused by pressure.'
http://math.ucr.edu/home/baez/einstein/einstein.pdf" by J C Baez and E F Bunn, page 7

Considering the collapse of a neutron star into a black hole is relative to the escape velocity exceeding c, the above implies that the escape velocity equation could be based on active mass, $m=V(\rho+3P/c^2)$.

(3) http://en.wikipedia.org/wiki/Escape_velocity#Calculating_an_escape_velocity